In the years after warning labels were pw on cigarette packs. the number of smokers

In Exercises 1-16. solve and check each linear equation. 7x - 5 - 72

In Exercises 1-16. solve and check each linear equation. 6x - 3 - 63

In Exercises 1-16. solve and check each linear equation. llx - (6x - 5) - 40

In Exercises 1-16. solve and check each linear equation. 5x - (2x - 10) - 35

In Exercises 1-16. solve and check each linear equation. 2x - 7 - 6+x

In Exercises 1-16. solve and check each linear equation. 3x + 5 - 2x + 13

In Exercises 1-16. solve and check each linear equation. 7x + 4 - x + 16

In Exercises 1-16. solve and check each linear equation. 13x + 14 - 12x - 5

In Exercises 1-16. solve and check each linear equation. 3~t - 2) + 7 - 2(.t + 5)

In Exercises 1-16. solve and check each linear equation. 2(x - 1) + 3 - x - 3(x + 1)

In Exercises 1-16. solve and check each linear equation. 3(x - 4) - 4(x - 3) - x + 3 - (x - 2)

In Exercises 1-16. solve and check each linear equation. 2 - (7x + 5) - 13 - 3x

In Exercises 1-16. solve and check each linear equation. 16 - 3(x - 1) - (x - 7)

In Exercises 1-16. solve and check each linear equation. 5x - (2t + 2) - x + (3x - 5)

In Exercises 1-16. solve and check each linear equation. 25 - (2 + 5y - 3(y + 2)] - - 3(2y - 5) - (5(v - 1) - 3y + 3]

In Exercises 1-16. solve and check each linear equation. 45 - (4 - 2y - 4(y + 7)] - - 4(1 + 3y) - [4 - 3(y + 2) - 2(2y - 5)]

Exercises 17-30 contain linear equations with constants in denominators. Solve each equation. XX XX XX 3 - 2 - 2

Exercises 17-30 contain linear equations with constants in denominators. Solve each equation. XX XX 3 - 2 - 2 5 - 6 + 1

Exercises 17-30 contain linear equations with constants in denominators. Solve each equation. 20 - 3 - 2

Exercises 17-30 contain linear equations with constants in denominators. Solve each equation. :. - .!. - :!. 5 2 6

Exercises 17-30 contain linear equations with constants in denominators. Solve each equation. 3x 2r 1 22. x2 _ _ 34x +5 s - 3 +

Exercises 17-30 contain linear equations with constants in denominators. Solve each equation. x2 _ _ 34x +5

Exercises 17-30 contain linear equations with constants in denominators. Solve each equation.

Exercises 17-30 contain linear equations with constants in denominators. Solve each equation. 2< :!: +.!2 7 2 2

Exercises 17-30 contain linear equations with constants in denominators. Solve each equation.

Exercises 17-30 contain linear equations with constants in denominators. Solve each equation. x+1 1 2 - x - 4- - 6+ - 3-

Exercises 17-30 contain linear equations with constants in denominators. Solve each equation.

Exercises 17-30 contain linear equations with constants in denominators. Solve each equation. 5+ - - - - -- 3 8

Exercises 17-30 contain linear equations with constants in denominators. Solve each equation. .t+l . x+2

Exercises 17-30 contain linear equations with constants in denominators. Solve each equation. 3x x - 3 x+2 --r- ~

Exercises 31-50 contain rational equations with variables in denominators. For each equation. a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variablrt. b. Keeping the restrictions in mind1 solve the equation. 4 5 - - - + 3 x 2r

Exercises 31-50 contain rational equations with variables in denominators. For each equation. a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variablrt. b. Keeping the restrictions in mind1 solve the equation. 5 10 ~4 x 3x

Exercises 31-50 contain rational equations with variables in denominators. For each equation. a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variablrt. b. Keeping the restrictions in mind1 solve the equation. 2 ... 5 13 33. - +.> - ,-+ - X _r 4

Exercises 31-50 contain rational equations with variables in denominators. For each equation. a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variablrt. b. Keeping the restrictions in mind1 solve the equation. 7 5 22 34. -;;- ~ 2x .>X .>

Exercises 31-50 contain rational equations with variables in denominators. For each equation. a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variablrt. b. Keeping the restrictions in mind1 solve the equation. 2 I Ill 3~ - +-- - -- 3x 4 6x 3

Exercises 31-50 contain rational equations with variables in denominators. For each equation. a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variablrt. b. Keeping the restrictions in mind1 solve the equation. 5 8 l 2; _ 9 _ i8 _ 3;

Exercises 31-50 contain rational equations with variables in denominators. For each equation. a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variablrt. b. Keeping the restrictions in mind1 solve the equation. x - 2 x+1 . - ?- +1 - -- _r x

Exercises 31-50 contain rational equations with variables in denominators. For each equation. a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variablrt. b. Keeping the restrictions in mind1 solve the equation. ~ _ ~ _ 7x _- 4 X ) )X

Exercises 31-50 contain rational equations with variables in denominators. For each equation. a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variablrt. b. Keeping the restrictions in mind1 solve the equation. 1 - + 5 - _ 1_1_ x - 1 x - 1

Exercises 31-50 contain rational equations with variables in denominators. For each equation. a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variablrt. b. Keeping the restrictions in mind1 solve the equation. 3 - - 7 - ..2.. x+4 x+4

Exercises 31-50 contain rational equations with variables in denominators. For each equation. a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variablrt. b. Keeping the restrictions in mind1 solve the equation. Bx 8 --- 4 - -- x+l x+l

Exercises 31-50 contain rational equations with variables in denominators. For each equation. a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variablrt. b. Keeping the restrictions in mind1 solve the equation. 2 X 4? ------? - x - 2 x - 2

Exercises 31-50 contain rational equations with variables in denominators. For each equation. a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variablrt. b. Keeping the restrictions in mind1 solve the equation. 3 1 2 --+- - -- 2< - 2 2 x - 1

Exercises 31-50 contain rational equations with variables in denominators. For each equation. a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variablrt. b. Keeping the restrictions in mind1 solve the equation. 3 5 1 ' --x+3 - 2t+6 --+--x - 2

Exercises 31-50 contain rational equations with variables in denominators. For each equation. a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variablrt. b. Keeping the restrictions in mind1 solve the equation. 3- + _ 2 - - -:--:::7:8--:::- x + 2 x - 2 (x + 2)(x 2)

Exercises 31-50 contain rational equations with variables in denominators. For each equation. a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variablrt. b. Keeping the restrictions in mind1 solve the equation. 5 3 12 --+--- . x + 2 x - 2 (x + 2)(x

Exercises 31-50 contain rational equations with variables in denominators. For each equation. a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variablrt. b. Keeping the restrictions in mind1 solve the equation. 2 _ _ _ 1 _ _ _ 2_r _ x+1 x - 1 x.2 - 1

Exercises 31-50 contain rational equations with variables in denominators. For each equation. a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variablrt. b. Keeping the restrictions in mind1 solve the equation. 4 2 32 -- + --- .,.:.~ X+ 5 X - 5 x 2 25

Exercises 31-50 contain rational equations with variables in denominators. For each equation. a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variablrt. b. Keeping the restrictions in mind1 solve the equation. 1 5 6 --- --- -,,--7---:: x - 4 x+2 x- 2r - 8

Exercises 31-50 contain rational equations with variables in denominators. For each equation. a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variablrt. b. Keeping the restrictions in mind1 solve the equation. 6 _ _ ..2._ _ - 20 ' x +3 x - 2 x 2 +x - 6

In Exercises 51-56, find all values of.r satifying the given conditions. y1 - 5(2t - 8) - 2,y2 - 5(x - 3) + 3, and y1 - y2

In Exercises 51-56, find all values of.r satifying the given conditions. y1 - 7(1t - 2) + 5,y2 - 6(2t - 1) + 24, and y1 - y2

In Exercises 51-56, find all values of.r satifying the given conditions. '1 - -sY -- 4 - , and y. - y, - 1.

In Exercises 51-56, find all values of.r satifying the given conditions. Y1 - --4 Yo - -- and )'I - )'2 - - 4.

In Exercises 51-56, find all values of.r satifying the given conditions. y 1 - -- y, - -- y - and x+4'- x+3 ' 3 .t2 + 7x+l2. Y1 + Y2 - YJ

In Exercises 51-56, find all values of.r satifying the given conditions. )'1 - x' + 2t _ 8 , y, - ;-:;:-4 y, - :;:-:-2 and Yl + y, - y,.

In Exercises 57-60, find all values of x such that y - 0. y - 4[x - (3 - .t)] - 7(x + I)

In Exercises 57-60, find all values of x such that y - 0. y - 2f1t - (4x - 6)] - 5(x - 6)

In Exercises 57-60, find all values of x such that y - 0. x + 6 _ _ s _ _ !_ 3x 12 x - 4 3

In Exercises 57-60, find all values of x such that y - 0. ~ :>.t + ) .t + l .)

In Exercises 61-68, solve each equation. Then determine whether the equation is an itlentiJy, a conditional equation, or an inconsistent equation. 5x + 9 - 9(x + 1) - 4x

In Exercises 61-68, solve each equation. Then determine whether the equation is an itlentiJy, a conditional equation, or an inconsistent equation. 4x + 7 - 7(x + I) - 3x

In Exercises 61-68, solve each equation. Then determine whether the equation is an itlentiJy, a conditional equation, or an inconsistent equation. 3(x + 2) - 7 + 1t

In Exercises 61-68, solve each equation. Then determine whether the equation is an itlentiJy, a conditional equation, or an inconsistent equation. 4(x + 5) - 21 + 4x

In Exercises 61-68, solve each equation. Then determine whether the equation is an itlentiJy, a conditional equation, or an inconsistent equation. lOx+ 3 - 8x + 3

In Exercises 61-68, solve each equation. Then determine whether the equation is an itlentiJy, a conditional equation, or an inconsistent equation. 5x + 7 - 2.r+7

In Exercises 61-68, solve each equation. Then determine whether the equation is an itlentiJy, a conditional equation, or an inconsistent equation. 2t 6 --3 - --3 + 4

In Exercises 61-68, solve each equation. Then determine whether the equation is an itlentiJy, a conditional equation, or an inconsistent equation. 3 X 7=3 - 7=3 + 3

The equations in Exercises 69-80 combine the types of equations we have discussed in this se<tion. Solve each equation. Then state whether the equation is an idemiJy, a c.onditional equation, or an inconsistent equation. .t ; 5 - 4 - 2t; 1

The equations in Exercises 69-80 combine the types of equations we have discussed in this se<tion. Solve each equation. Then state whether the equation is an idemiJy, a c.onditional equation, or an inconsistent equation. x+2 . x+l

The equations in Exercises 69-80 combine the types of equations we have discussed in this se<tion. Solve each equation. Then state whether the equation is an idemiJy, a c.onditional equation, or an inconsistent equation. 2 X 71. --- 3 + - x - 2 x - 2

The equations in Exercises 69-80 combine the types of equations we have discussed in this se<tion. Solve each equation. Then state whether the equation is an idemiJy, a c.onditional equation, or an inconsistent equation. 6 - 2t 72. --+ 2 - --, x + 3 x + .>

The equations in Exercises 69-80 combine the types of equations we have discussed in this se<tion. Solve each equation. Then state whether the equation is an idemiJy, a c.onditional equation, or an inconsistent equation. S.t - (3x + 2) + 10 - 3x

The equations in Exercises 69-80 combine the types of equations we have discussed in this se<tion. Solve each equation. Then state whether the equation is an idemiJy, a c.onditional equation, or an inconsistent equation. 2(x + 2) + 2t - 4(x + 1)

The equations in Exercises 69-80 combine the types of equations we have discussed in this se<tion. Solve each equation. Then state whether the equation is an idemiJy, a c.onditional equation, or an inconsistent equation. 2 1 3 - +- - - X 2 4

The equations in Exercises 69-80 combine the types of equations we have discussed in this se<tion. Solve each equation. Then state whether the equation is an idemiJy, a c.onditional equation, or an inconsistent equation. 3 I 1 - - - - - x 6 3

The equations in Exercises 69-80 combine the types of equations we have discussed in this se<tion. Solve each equation. Then state whether the equation is an idemiJy, a c.onditional equation, or an inconsistent equation. 4 3 7 --+ --- ~-,i-:--= x - 2 x + 5 (x + 5)(x 2)

The equations in Exercises 69-80 combine the types of equations we have discussed in this se<tion. Solve each equation. Then state whether the equation is an idemiJy, a c.onditional equation, or an inconsistent equation. x - I (2x + 3)(x - I) 2t + 3

The equations in Exercises 69-80 combine the types of equations we have discussed in this se<tion. Solve each equation. Then state whether the equation is an idemiJy, a c.onditional equation, or an inconsistent equation. __!.L 4x 36 ' :r+3 .r - 3 .r2 9

The equations in Exercises 69-80 combine the types of equations we have discussed in this se<tion. Solve each equation. Then state whether the equation is an idemiJy, a c.onditional equation, or an inconsistent equation. 4 3 , - , 2 X' + 1t - 10 X' + X - 6 X - X - 12

In Exercises 81-84. Use the Y=I screen to write the equation being solved. Then me the table to soh:e the equation. f'loU f'loU' tloU: ,y~ ,y~ s ~g:~~~ - 'Yl= w X V1 ~ , -.,. W~= -~ " '18 18 W6= '1 1s n ,y'E. 6 -u 1 ' ., 0 ~ ., ., 3 ) -n P<=-3

In Exercises 81-84. Use the Y=I screen to write the equation being solved. Then me the table to soh:e the equation. f'lot1 f'lot~ tloU: 'Y1 ~~~3-S) ,y~ s + Wl= 1\ V1 ~ ,y, - 63 Ws= " " " 7l Ws= 15 75 77 'Y7= .. 81 17 ta 87 07 ~ l9 '3 99 07 '~ 11t=13

In Exercises 81-84. Use the Y=I screen to write the equation being solved. Then me the table to soh:e the equation. ~~~ 5~~~;?' , y) X Y1 y~ ,y, -l2 1S w~~ -.s 1M 1U w. 0 10 ::Y.l! .s 7.5 7.$ 1 1.S .S ts 2 ) 0 X= " 1

In Exercises 81-84. Use the Y=I screen to write the equation being solved. Then me the table to soh:e the equation. f'loU f'lon tloU: ,y1 ,y~ s 1~~~-+ I~-? - 'Yl= w X V1 ~ , -' 7 to W~= ... &.8 a,,a W6= .a -u 7.5 ,y'E. .7 &.'t ., ... ... &.2: s.z .s ., ., -.- -s.e -u P<= -1

Evaluate x 2 - x for the value of x satisfying 4(x - 2) + 2 - 4x - 2(2 - x).

Evaluate x 2 - x for the value of x satisfying 2(x - 6) - 3x + 2(2t - 1).

Evaluate x2 - (xy - y) for x satisfying 3 (x; 3 ) - 2t + 6 andy satisfying - 2y - 10 - Sy + 18.

Evaluatex' - (xy - y) for x satisfying 13x 4 - 6 - 5x + 2 andy satisfying 5 - y - 7(y + 4) + 1.

In Exercises 89-96, solve each equation. ((3 + 6)2 + 3)4 - - 54x

In Exercises 89-96, solve each equation. 23 - (4(5 - 3)3 ] - - S.t

In Exercises 89-96, solve each equation. 5 - 12t - 8 - 7x - [6 ~ 3(2 + 53) + 5x]

In Exercises 89-96, solve each equation. 2(5x + 58) - lOx+ 4(21 + 3.5 - 11)

In Exercises 89-96, solve each equation. 0.7x + 0.4(20) - 0.5(x + 20)

In Exercises 89-96, solve each equation. 0.5(x + 2) - 0.1 + 3(0.1x + 0.3)

In Exercises 89-96, solve each equation. 4x + 13 - (2< - [4(x - 3) - 5]1 - 2(x - 6)

In Exercises 89-96, solve each equation. - 2(7 - [4 - 2(1 - x) + 3]1 - 10 - f4x - 2(x - 3)]

In the years after warning labels were pw on cigarette packs. the number of smokers dropped from approximately two in Jive adults to one in five. 111e bar graph shows the percentage of American adults who smoked cigarettes for selecled years from 1970 through 2010. 40% 30% 20% 10% Percentage of Ame-.rican Adults Who Smoke Cigarettes 19% 1970 1980 1990 2000 2010 Year Source: Ce.nters for Disease Control and Prevention The nwthematic.af model X p + - - 37 2 describes the percentage of Americans who smoked cigarettes, p. x years after 1970. Use this model to solve tercises 97-98. a. Does the mathematical model underestimateoroverestimate the percentage of American aduJts who smoked cigarettes in 2010? By how mucll? b. Use the mathematical model 10 project Lhe year when only 7% of American adults will smoke cigarettes.

In the years after warning labels were pw on cigarette packs. the number of smokers dropped from approximately two in Jive adults to one in five. 111e bar graph shows the percentage of American adults who smoked cigarettes for selecled years from 1970 through 2010. 40% 30% 20% 10% Percentage of Ame-.rican Adults Who Smoke Cigarettes 19% 1970 1980 1990 2000 2010 Year Source: Ce.nters for Disease Control and Prevention The nwthematic.af model X p + - - 37 2 describes the percentage of Americans who smoked cigarettes, p. x years after 1970. Use this model to solve tercises 97-98. a. Does the mathematical model underestimateoroverestimate the percentage of American aduJts who smoked cigarettes in 2000? By how much? b. Usc the mathematical model to project the year when only 2% of American adults will smoke cigarettes..

The line graph shows the cost of inflation. What cost $10,000 in 1967 would cost the amoulll shown by the graph in subsequelll year.t (111e symbol...,._ on the horizontal axis shoh'S that there is a break in values between 0 and 80. Tlws, the first tiik mark on the horizontal axis represents 1980.) 70 60 50 40 30 20 10 The Cost of IoDation Whlf cost you $10,000 ia 1967 wofl ml p tkis 11tdt i sukequent yutt. $24,900 t980 l%"5 1990 t995 2000 2005 1 ., Year 2008 Source: U.S. Burea ~ Labor Statistics Here are fwo mathematic-lit models for the data shown by the graph. In each formula. C represetlls the cost x years after 1980 of what cost $10,000 inl967. Modt-1 1 C - 1388x + 24,963 Model t c - 3x' + 1308.< + 25,268 Use these models to solve Exerdses 99-102. a. Use the graph to estimate the cost in 2000~ to t he nearest thousand dollars, or what cost $10.000 in 1967. b. Use model 1 to detem1ine the cost in 2000. How well does this describe your estimate from part (a)? c. Use model 2 to detem1ine the cost in 2000. How well does this describe your estimate from part (a)?

The line graph shows the cost of inflation. What cost $10,000 in 1967 would cost the amoulll shown by the graph in subsequelll year.t (111e symbol...,._ on the horizontal axis shoh'S that there is a break in values between 0 and 80. Tlws, the first tiik mark on the horizontal axis represents 1980.) 70 60 50 40 30 20 10 The Cost of IoDation Whlf cost you $10,000 ia 1967 wofl ml p tkis 11tdt i sukequent yutt. $24,900 t980 l%"5 1990 t995 2000 2005 1 ., Year 2008 Source: U.S. Burea ~ Labor Statistics Here are fwo mathematic-lit models for the data shown by the graph. In each formula. C represetlls the cost x years after 1980 of what cost $10,000 inl967. Modt-1 1 C - 1388x + 24,963 Model t c - 3x' + 1308.< + 25,268 Use these models to solve Exerdses 99-102. a~ Usc the graph to e.stimate the oost in 1990, to the nearest thousand dollars. or what cost $10,000 in 1967. b. Usc model 1 to detennine the cost in 1990. How well does this describe your estimate from part (a)? c. Use model 2 to detem1ine the cost in 1990. How well does this describe your estimate from part (a)?

The line graph shows the cost of inflation. What cost $10,000 in 1967 would cost the amoulll shown by the graph in subsequelll year.t (111e symbol...,._ on the horizontal axis shoh'S that there is a break in values between 0 and 80. Tlws, the first tiik mark on the horizontal axis represents 1980.) 70 60 50 40 30 20 10 The Cost of IoDation Whlf cost you $10,000 ia 1967 wofl ml p tkis 11tdt i sukequent yutt. $24,900 t980 l%"5 1990 t995 2000 2005 1 ., Year 2008 Source: U.S. Burea ~ Labor Statistics Here are fwo mathematic-lit models for the data shown by the graph. In each formula. C represetlls the cost x years after 1980 of what cost $10,000 inl967. Modt-1 1 C - 1388x + 24,963 Model t c - 3x' + 1308.< + 25,268 Use these models to solve Exerdses 99-102. Use model 1 to dete rmine in which year the cost will be S77.707 ror what cost $10.000 in 1967.

The line graph shows the cost of inflation. What cost $10,000 in 1967 would cost the amoulll shown by the graph in subsequelll year.t (111e symbol...,._ on the horizontal axis shoh'S that there is a break in values between 0 and 80. Tlws, the first tiik mark on the horizontal axis represents 1980.) 70 60 50 40 30 20 10 The Cost of IoDation Whlf cost you $10,000 ia 1967 wofl ml p tkis 11tdt i sukequent yutt. $24,900 t980 l%"5 1990 t995 2000 2005 1 ., Year 2008 Source: U.S. Burea ~ Labor Statistics Here are fwo mathematic-lit models for the data shown by the graph. In each formula. C represetlls the cost x years after 1980 of what cost $10,000 inl967. Modt-1 1 C - 1388x + 24,963 Model t c - 3x' + 1308.< + 25,268 Use these models to solve Exerdses 99-102. Use model 1 to dete rmine in which year the cost will be SS0.483 ror what cost $10.000 in 1967 . .

Formulas with rational expressions are often used to model leaming. Many of these formulas model the proportion of correct responses in ferms of the number of trials of a panicular task. One such model. called a learning curve, is p _ 0.9x - 0.4 0.9x + 0.1' where Pis the proponion of correct responses after x trials. If P - 0, there are no correct responses. If P - I, all responses are correct. The graph of the rational Jonmda is shown. Use the Jonnula to solve Exerdses 103-104. p A Learning Curve 1.0 0.9 0.8 0.7 0.6 0.5 0.4 OJ 0.2 0.1 P - 0.9x - 0.4 - o.9x + 0.1 ~~~~~~~~~~~~~~~~X 1 2 3 4 5 6 7 8 9 10 I I 12 13 14 15 Number or Learning liials How many learning trials are necessary for 0.95 of the responses to be correct? Identify your solution as a point on the graph.

Formulas with rational expressions are often used to model leaming. Many of these formulas model the proportion of correct responses in ferms of the number of trials of a panicular task. One such model. called a learning curve, is p _ 0.9x - 0.4 0.9x + 0.1' where Pis the proponion of correct responses after x trials. If P - 0, there are no correct responses. If P - I, all responses are correct. The graph of the rational Jonmda is shown. Use the Jonnula to solve Exerdses 103-104. p A Learning Curve 1.0 0.9 0.8 0.7 0.6 0.5 0.4 OJ 0.2 0.1 P - 0.9x - 0.4 - o.9x + 0.1 ~~~~~~~~~~~~~~~~X 1 2 3 4 5 6 7 8 9 10 I I 12 13 14 15 Number or Learning liials How many learning trials are nece.~sary for 0.5 o f the responses to be correc-t'! Identify your solution as a point on the graph .

A company wants to increase the 10% peroxide content of its product by adding pure peroxide (1 00% peroxide). If x lite rs of pure peroxide are added to 500 liter.; of its 10% solution, the concentration, C, of the new mixture is given by X+ 0.1(500) c - -oo .t+) How many liter.; of pure peroxide should be added to produce a new product that is 28% peroxide?

Suppose that x liters of pure acid are added to 200 lite rs of a 35% acid solution. a. Write a fommla tha t gives the concentration, C, of the new mixture. (Hint: See Exercise 105.) b. How many liter.; of pure acid should be added to produce a new mixture that is 74% acid?

What is a linear equation in one variable. Give an example of this type of equation.

Suppose that vou solve I -I -I by multipl);ng both sides by 10 rather than the least common denominator (namely. 10). Describe what ha n~ If you gel the correct solution, why do you think \llC clear the equation of fractions by multiplying by the feast common denominator?

Suppose you a re an algebra teacher grading the following solution on an examination: - 3(x - 6) - 2 - x - 3x - 18 - 2 - x - 2r - 18 - 2 - 2r - - 16 X - 8. You should note that 8 c.hecks, so the solution set is ISJ. The student who worked the problem therefore wants full credit. Can you find any errors in the solution? If full credit is 10 points. how many poinl'i should you give the student? Justify your position.

Explain how to find restrictions on the variable in a rational equation.

Why should restrictions on the variable in a rational equation be listed before you begin solving the equation?

What is an identity? Give an example.

What is a conditional equation? Give an example.

What is an inconsistent equation? Give an example.

Describe the trend shown by the graph in Exercises 103- 104 in terms of learning new tasks. What happens initially and what happens as time increases?

In Exercises 116-119. use your graphing utility to enter each side of the equation .separalely under y 1 and y2 Then use the utility's IT ABLE! or !GRAPH I feature to so/Ye the equatioll. 5x + 2(x - I) - 3x + 10

In Exercises 116-119. use your graphing utility to enter each side of the equation .separalely under y 1 and y2 Then use the utility's IT ABLE! or !GRAPH I feature to so/Ye the equatioll. 2r + 3(x - 4) - 4x - 7

In Exercises 116-119. use your graphing utility to enter each side of the equation .separalely under y 1 and y2 Then use the utility's IT ABLE! or !GRAPH I feature to so/Ye the equatioll. x - 3 x - 5 --- I - -- 5 4

In Exercises 116-119. use your graphing utility to enter each side of the equation .separalely under y 1 and y2 Then use the utility's IT ABLE! or !GRAPH I feature to so/Ye the equatioll. 2t - l x - 5 x - 3 n g. - 3- - - 6 - - - 4-

In Exercises 120--123, determine whether each stalement makes sense or does not make swse, and explaitJ your reasoning. The model P - - 0.18/l + 2.1 describes the number of pay phones, P, in millions.n years after 2000, so I ha,1e to solve a linear equation to determine Lhe number o f pay phones in 2010.

In Exercises 120--123, determine whether each stalement makes sense or does not make swse, and explaitJ your reasoning. Although r ca n solve 3x + i - ! by firsl subtracti g~ from both sides, I fi nd it easier to begin by multiplying both sides by 20, the least common denominator.

In Exercises 120--123, determine whether each stalement makes sense or does not make swse, and explaitJ your reasoning. Beca.use I know how to clear an equation of fractions, I decided to clear the equation 0.5x + 8.3 - I 2.4 of decimals by multiplying both sides by 10.

In Exercises 120--123, determine whether each stalement makes sense or does not make swse, and explaitJ your reasoning. Because x - x + 5 is an inconsistent equation, the graphs o f y - x andy - x + 5 should not intersect

In Exercises 124-127, determine whether each statement is true or false. If the statement is false, make the necessary dwnge(s) to produce a true statement. llle equation - ?x - x has no solution.

In Exercises 124-127, determine whether each statement is true or false. If the statement is false, make the necessary dwnge(s) to produce a true statement. Th . X 4 d . 1 . c equattons --4 - --4 an x - 4 are equJvalent.

In Exercises 124-127, determine whether each statement is true or false. If the statement is false, make the necessary dwnge(s) to produce a true statement. The equations 3y - 1 - 11 a nd 3y - 7 - 5 are equi\'alcnt.

In Exercises 124-127, determine whether each statement is true or false. If the statement is false, make the necessary dwnge(s) to produce a true statement. faand reany lnumbe~t en ax + b - Oalways has one number in its solution set.

If x represents a number, write an English sentence about the number that results in an inconsistent equation.

F. d b h I ?x + 4 3 h . m . sue 1 1at - b- + 1 - x as a solution set gtven by 1- 6).

Find b such that 4 x - 5 b - 3 has a solution set given by 0.

Exercises 131-133 will help you prepare for the material covered in the next section. Jane's salary exceeds Jim's by $150 per week.lf x represents Jim's weekly salary, write an algebraic expression that models Jane's weekly salary.

Exercises 131-133 will help you prepare for the material covered in the next section. A telephone lexting plan has a monthly fee o f $20 with a charge o f S0.05 per text. Write an a lgebraic expression that models the plan's monthly cost for x text messages.

Exercises 131-133 will help you prepare for the material covered in the next section. If the width of a rectangle is represented by x and the length is represented by x + 200, write a simplifie.d a lgebraic expression that models the rectangle's pe rimeter.