 6.2.1: Fill in each blank so that the resulting statement is true.An equat...
 6.2.2: Fill in each blank so that the resulting statement is true.Two or m...
 6.2.3: Fill in each blank so that the resulting statement is true.The addi...
 6.2.4: Fill in each blank so that the resulting statement is true.The mult...
 6.2.5: Fill in each blank so that the resulting statement is true.The firs...
 6.2.6: Fill in each blank so that the resulting statement is true.The alge...
 6.2.7: Fill in each blank so that the resulting statement is true.The equa...
 6.2.8: Fill in each blank so that the resulting statement is true.A statem...
 6.2.9: Fill in each blank so that the resulting statement is true.The cros...
 6.2.10: Fill in each blank so that the resulting statement is true.In solvi...
 6.2.11: Fill in each blank so that the resulting statement is true.In solvi...
 6.2.12: Fill in each blank so that the resulting statement is true.In 1215,...
 6.2.13: Fill in each blank so that the resulting statement is true.In 1215,...
 6.2.14: Fill in each blank so that the resulting statement is true.In 1215,...
 6.2.15: Fill in each blank so that the resulting statement is true.In 1215,...
 6.2.16: In 158, solve and check each equation.5x  8 = 72
 6.2.17: In 158, solve and check each equation.. 4x  14 = 82
 6.2.18: In 158, solve and check each equation.9x  14 = 77
 6.2.19: In 158, solve and check each equation.14  5x = 41
 6.2.20: In 158, solve and check each equation.25  6x = 83
 6.2.21: In 158, solve and check each equation.14  5x = 419(5x  2) = 45
 6.2.22: In 158, solve and check each equation.. 10(3x + 2) = 70
 6.2.23: In 158, solve and check each equation.5x  (2x  10) = 35
 6.2.24: In 158, solve and check each equation.11x  (6x  5) = 40
 6.2.25: In 158, solve and check each equation.3x + 5 = 2x + 13
 6.2.26: In 158, solve and check each equation.2x  7 = 6 + x
 6.2.27: In 158, solve and check each equation.. 8x  2 = 7x  5
 6.2.28: In 158, solve and check each equation.13x + 14 = 5 + 12x
 6.2.29: In 158, solve and check each equation.7x + 4 = x + 16
 6.2.30: In 158, solve and check each equation.8x + 1 = x + 43
 6.2.31: In 158, solve and check each equation.. 8y  3 = 11y + 9
 6.2.32: In 158, solve and check each equation.5y  2 = 9y + 2
 6.2.33: In 158, solve and check each equation.2(4  3x) = 2(2x + 5)
 6.2.34: In 158, solve and check each equation.3(5  x) = 4(2x + 1)
 6.2.35: In 158, solve and check each equation.8(y + 2) = 2(3y + 4)
 6.2.36: In 158, solve and check each equation.3(3y  1) = 4(3 + 3y)
 6.2.37: In 158, solve and check each equation.3(x + 1) = 7(x  2)  3
 6.2.38: In 158, solve and check each equation.5x  4(x + 9) = 2x  3
 6.2.39: In 158, solve and check each equation.5(2x  8)  2 = 5(x  3) + 3
 6.2.40: In 158, solve and check each equation.7(3x  2) + 5 = 6(2x  1) + 24
 6.2.41: In 158, solve and check each equation.6 = 4(1  x) + 3(x + 1)
 6.2.42: In 158, solve and check each equation.100 = (x  1) + 4(x  6)
 6.2.43: In 158, solve and check each equation.10(z + 4)  4(z  2) = 3(z  ...
 6.2.44: In 158, solve and check each equation.2(z  4)  (3z  2) = 2  (...
 6.2.45: In 158, solve and check each equation.2x3  5 = 7
 6.2.46: In 158, solve and check each equation.3x4  9 = 6
 6.2.47: In 158, solve and check each equation.x3+ x2 = 56
 6.2.48: In 158, solve and check each equation.x4  x5 = 1
 6.2.49: In 158, solve and check each equation.20  z3 = z2
 6.2.50: In 158, solve and check each equation.z5  12 = z6
 6.2.51: In 158, solve and check each equation.y3+25 = y5  25
 6.2.52: In 158, solve and check each equation.y12+16 = y2  14
 6.2.53: In 158, solve and check each equation.3x4  3 = x2+ 2
 6.2.54: In 158, solve and check each equation.3x5  25 = x3+25
 6.2.55: In 158, solve and check each equation.3x5  x = x10  52
 6.2.56: In 158, solve and check each equation.2x  2x7 = x2+172
 6.2.57: In 158, solve and check each equation.x  35  1 = x  54
 6.2.58: In 158, solve and check each equation.x  23  4 = x + 1
 6.2.59: In 5972, solve each proportion and check.
 6.2.60: In 5972, solve each proportion and check.
 6.2.61: In 5972, solve each proportion and check.
 6.2.62: In 5972, solve each proportion and check.
 6.2.63: In 5972, solve each proportion and check.
 6.2.64: In 5972, solve each proportion and check.
 6.2.65: In 5972, solve each proportion and check.
 6.2.66: In 5972, solve each proportion and check.
 6.2.67: In 5972, solve each proportion and check.
 6.2.68: In 5972, solve each proportion and check.
 6.2.69: In 5972, solve each proportion and check.
 6.2.70: In 5972, solve each proportion and check.
 6.2.71: In 5972, solve each proportion and check.
 6.2.72: In 5972, solve each proportion and check.
 6.2.73: In 7392, solve each equation. Use set notation to express solution ...
 6.2.74: In 7392, solve each equation. Use set notation to express solution ...
 6.2.75: In 7392, solve each equation. Use set notation to express solution ...
 6.2.76: In 7392, solve each equation. Use set notation to express solution ...
 6.2.77: In 7392, solve each equation. Use set notation to express solution ...
 6.2.78: In 7392, solve each equation. Use set notation to express solution ...
 6.2.79: In 7392, solve each equation. Use set notation to express solution ...
 6.2.80: In 7392, solve each equation. Use set notation to express solution ...
 6.2.81: In 7392, solve each equation. Use set notation to express solution ...
 6.2.82: In 7392, solve each equation. Use set notation to express solution ...
 6.2.83: In 7392, solve each equation. Use set notation to express solution ...
 6.2.84: In 7392, solve each equation. Use set notation to express solution ...
 6.2.85: In 7392, solve each equation. Use set notation to express solution ...
 6.2.86: In 7392, solve each equation. Use set notation to express solution ...
 6.2.87: In 7392, solve each equation. Use set notation to express solution ...
 6.2.88: In 7392, solve each equation. Use set notation to express solution ...
 6.2.89: In 7392, solve each equation. Use set notation to express solution ...
 6.2.90: In 7392, solve each equation. Use set notation to express solution ...
 6.2.91: In 7392, solve each equation. Use set notation to express solution ...
 6.2.92: In 7392, solve each equation. Use set notation to express solution ...
 6.2.93: Evaluate x2  x for the value of x satisfying 4(x  2) + 2 = 4x  2...
 6.2.94: Evaluate x2  x for the value of x satisfying 2(x  6) = 3x + 2(2x ...
 6.2.95: Evaluate x2  (xy  y) for x satisfying x 5  2 = x 3 and y satisfy...
 6.2.96: Evaluate x2  (xy  y) for x satisfying 3x 2 + 3x 4 = x 4  4 and y...
 6.2.97: In 97104, solve each equation.. 3(3 + 6)2 , 34 # 4 = 54x
 6.2.98: In 97104, solve each equation.23  34(5  3)3 4 = 8x
 6.2.99: In 97104, solve each equation.5  12x = 8  7x  36 , 3(2 + 53) + 5x4
 6.2.100: In 97104, solve each equation.2(5x + 58) = 10x + 4(21 , 3.5  11)
 6.2.101: In 97104, solve each equation.. 0.7x + 0.4(20) = 0.5(x + 20)
 6.2.102: In 97104, solve each equation.0.5(x + 2) = 0.1 + 3(0.1x + 0.3)
 6.2.103: In 97104, solve each equation.4x + 13  52x  34(x  3)  546 = 2(x...
 6.2.104: In 97104, solve each equation.257  34  2(1  x) + 346 = 10  34x...
 6.2.105: The la guidelines, which apply to both men and women, give healthy ...
 6.2.106: In the years after warning labels were put on cigarette packs, the ...
 6.2.107: In the years after warning labels were put on cigarette packs, the ...
 6.2.108: In the years after warning labels were put on cigarette packs, the ...
 6.2.109: The volume of blood in a persons body is proportional to body weigh...
 6.2.110: The number of gallons of water used when taking a shower is proport...
 6.2.111: An alligators tail length is proportional to its body length. An al...
 6.2.112: An objects weight on the moon is proportional to its weight on Eart...
 6.2.113: St. Paul Island in Alaska has 12 fur seal rookeries (breeding place...
 6.2.114: To estimate the number of bass in a lake, wildlife biologists tagge...
 6.2.115: What is the solution set of an equation?
 6.2.116: State the addition property of equality and give an example.
 6.2.117: State the multiplication property of equality and give an example.
 6.2.118: What is a proportion? Give an example with your description
 6.2.119: Explain how to solve a proportion. Illustrate your explanation with...
 6.2.120: How do you know whether an equation has one solution, no solution, ...
 6.2.121: What is the difference between solving an equation such as 2(x  4)...
 6.2.122: Suppose that you solve x 5  x 2 = 1 by multiplying both sides by 2...
 6.2.123: Suppose you are an algebra teacher grading the following solution o...
 6.2.124: Although the formulas in Example 6 on page 356 are correct, some pe...
 6.2.125: Make Sense? In 125128, determine whether each statement makes sense...
 6.2.126: Make Sense? In 125128, determine whether each statement makes sense...
 6.2.127: Make Sense? In 125128, determine whether each statement makes sense...
 6.2.128: Make Sense? In 125128, determine whether each statement makes sense...
 6.2.129: Write three equations whose solution set is 556.
 6.2.130: If x represents a number, write an English sentence about the numbe...
 6.2.131: A womans height, h, is related to the length of the femur, f (the b...
Solutions for Chapter 6.2: Linear Equations in One Variable and Proportions
Full solutions for Thinking Mathematically  6th Edition
ISBN: 9780321867322
Solutions for Chapter 6.2: Linear Equations in One Variable and Proportions
Get Full SolutionsChapter 6.2: Linear Equations in One Variable and Proportions includes 131 full stepbystep solutions. Since 131 problems in chapter 6.2: Linear Equations in One Variable and Proportions have been answered, more than 70942 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Thinking Mathematically, edition: 6. Thinking Mathematically was written by and is associated to the ISBN: 9780321867322.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.