 1.1: In Exercises 112, solve each equation.5 + 3(x + 5) = 2(3x  4)
 1.2: In Exercises 112, solve each equation.5x2  2x = 7
 1.3: In Exercises 112, solve each equation.x  35  1 = x  54
 1.4: In Exercises 112, solve each equation.3x2  6x  2 = 0
 1.5: In Exercises 112, solve each equation.4x  2(1  x) = 3(2x + 1)  5
 1.6: In Exercises 112, solve each equation.5x2 + 1 = 37
 1.7: In Exercises 112, solve each equation.x(2x  3) = 4
 1.8: In Exercises 112, solve each equation.3x4  x3+ 1 = 4x5  320
 1.9: In Exercises 112, solve each equation.(x + 3)2 = 24
 1.10: In Exercises 112, solve each equation.1x2  4x + 1 = 0
 1.11: In Exercises 112, solve each equation.3x + 1  (x  5) = 2x  4
 1.12: In Exercises 112, solve each equation.2xx2 + 6x + 8 = xx + 4  2x + 2
 1.13: In Exercises 1317, find the xintercepts of the graph of eachequati...
 1.14: In Exercises 1317, find the xintercepts of the graph of eachequati...
 1.15: In Exercises 1317, find the xintercepts of the graph of eachequati...
 1.16: In Exercises 1317, find the xintercepts of the graph of eachequati...
 1.17: In Exercises 1317, find the xintercepts of the graph of eachequati...
 1.18: In Exercises 1819, find all values of x satisfying the givenconditi...
 1.19: In Exercises 1819, find all values of x satisfying the givenconditi...
 1.20: Solve by completing the square: x2 + 10x  3 = 0.
 1.21: In Exercises 2122, without solving the equation, determine thenumbe...
 1.22: In Exercises 2122, without solving the equation, determine thenumbe...
 1.23: In Exercises 2325, graph each equation in a rectangularcoordinate s...
 1.24: In Exercises 2325, graph each equation in a rectangularcoordinate s...
 1.25: In Exercises 2325, graph each equation in a rectangularcoordinate s...
 1.26: Solve for n: L = a + (n  1)d.
 1.27: Solve for l: A = 2lw + 2lh + 2wh
 1.28: Solve for f1: f = f1f2f1 + f2
 1.29: Although you want to choose a career that fits your interestsand ab...
 1.30: The line graph indicates that in 1960, 23% of U.S. taxes camefrom c...
 1.31: You invested $25,000 in two accounts paying 8% and 9%annual interes...
 1.32: The toll to a bridge costs $8. Commuters who use the bridgefrequent...
 1.33: After a 40% price reduction, you purchase a camcorder for $468.What...
 1.34: You invested $4000. On part of this investment, you earned4% intere...
 1.35: In Exercises 3536, find the dimensions of each rectangle.The rectan...
 1.36: In Exercises 3536, find the dimensions of each rectangle.The rectan...
 1.37: A vertical pole is supported by three wires. Each wire is13 yards l...
 1.38: a. The alligator, at one time an endangered species, was thesubject...
 1.39: A substantial percentage of the United States populationis foreign...
 1.40: In Exercises 4045, perform the indicated operations and writethe re...
 1.41: In Exercises 4045, perform the indicated operations and writethe re...
 1.42: In Exercises 4045, perform the indicated operations and writethe re...
 1.43: In Exercises 4045, perform the indicated operations and writethe re...
 1.44: In Exercises 4045, perform the indicated operations and writethe re...
 1.45: In Exercises 4045, perform the indicated operations and writethe re...
 1.46: In Exercises 4547, solve each formula for the specified variable.T ...
 1.47: In Exercises 4547, solve each formula for the specified variable.T ...
 1.48: In Exercises 4857, perform the indicated operations and write there...
 1.49: In Exercises 4857, perform the indicated operations and write there...
 1.50: In Exercises 4857, perform the indicated operations and write there...
 1.51: In Exercises 4857, perform the indicated operations and write there...
 1.52: In Exercises 4857, perform the indicated operations and write there...
 1.53: In Exercises 4857, perform the indicated operations and write there...
 1.54: In Exercises 4857, perform the indicated operations and write there...
 1.55: In Exercises 4857, perform the indicated operations and write there...
 1.56: In Exercises 4857, perform the indicated operations and write there...
 1.57: In Exercises 4857, perform the indicated operations and write there...
 1.58: Solve each equation in Exercises 5859 by factoring.2x2 + 15x = 8
 1.59: Solve each equation in Exercises 5859 by factoring.5x2 + 20x = 0
 1.60: Solve each equation in Exercises 6063 by the square root property.2...
 1.61: Solve each equation in Exercises 6063 by the square root property.x...
 1.62: Solve each equation in Exercises 6063 by the square root property.(...
 1.63: Solve each equation in Exercises 6063 by the square root property.(...
 1.64: In Exercises 6465, determine the constant that should be addedto th...
 1.65: In Exercises 6465, determine the constant that should be addedto th...
 1.66: Solve each equation in Exercises 6667 by completing the square.x2 ...
 1.67: Solve each equation in Exercises 6667 by completing the square.3x2 ...
 1.68: Solve each equation in Exercises 6870 using the quadraticformula.x2...
 1.69: Solve each equation in Exercises 6870 using the quadraticformula.x2...
 1.70: Solve each equation in Exercises 6870 using the quadraticformula.2x...
 1.71: In Exercises 7172, without solving the given quadratic equation,det...
 1.72: In Exercises 7172, without solving the given quadratic equation,det...
 1.73: Solve each equation in Exercises 7381 by the method of your choice....
 1.74: Solve each equation in Exercises 7381 by the method of your choice....
 1.75: Solve each equation in Exercises 7381 by the method of your choice....
 1.76: Solve each equation in Exercises 7381 by the method of your choice....
 1.77: Solve each equation in Exercises 7381 by the method of your choice....
 1.78: Solve each equation in Exercises 7381 by the method of your choice....
 1.79: Solve each equation in Exercises 7381 by the method of your choice....
 1.80: Solve each equation in Exercises 7381 by the method of your choice....
 1.81: Solve each equation in Exercises 7381 by the method of your choice....
 1.82: The formula W = 3t2 models the weight of a human fetus,W, in grams,...
 1.83: One possible reason for the explosion of college tuitioninvolves th...
 1.84: An architect is allowed 15 square yards of floor space to adda smal...
 1.85: A building casts a shadow that is double the height of thebuilding....
 1.86: Solve each polynomial equation in Exercises 8687.2x4 = 50x2
 1.87: Solve each polynomial equation in Exercises 8687.2x3  x2  18x + 9...
 1.88: Solve each radical equation in Exercises 8889.22x  3 + x = 3
 1.89: Solve each radical equation in Exercises 8889.2x  4 + 2x + 1 = 5
 1.90: Solve the equations with rational exponents in Exercises 9091.3x34 ...
 1.91: Solve the equations with rational exponents in Exercises 9091.(x  ...
 1.92: Solve each equation in Exercises 9293 by making an appropriatesubst...
 1.93: Solve each equation in Exercises 9293 by making an appropriatesubst...
 1.94: Solve the equations containing absolute value in Exercises 9495. 2x...
 1.95: Solve the equations containing absolute value in Exercises 9495.2 x...
 1.96: Solve each equation in Exercises 96102 by the method of yourchoice....
 1.97: Solve each equation in Exercises 96102 by the method of yourchoice....
 1.98: Solve each equation in Exercises 96102 by the method of yourchoice....
 1.99: Solve each equation in Exercises 96102 by the method of yourchoice....
 1.100: Solve each equation in Exercises 96102 by the method of yourchoice....
 1.101: Solve each equation in Exercises 96102 by the method of yourchoice....
 1.102: Solve each equation in Exercises 96102 by the method of yourchoice....
 1.103: Long before the Supreme Court decision legalizing marriagebetween p...
 1.104: In Exercises 104106, express each interval in setbuilder notationa...
 1.105: In Exercises 104106, express each interval in setbuilder notationa...
 1.106: In Exercises 104106, express each interval in setbuilder notationa...
 1.107: In Exercises 107110, use graphs to find each set.(2, 1] [1, 3)
 1.108: In Exercises 107110, use graphs to find each set.(2, 1] [1, 3)
 1.109: In Exercises 107110, use graphs to find each set.[1, 3) (0, 4)
 1.110: In Exercises 107110, use graphs to find each set.[1, 3) (0, 4)
 1.111: In Exercises 111121, solve each inequality. Other than , useinterva...
 1.112: In Exercises 111121, solve each inequality. Other than , useinterva...
 1.113: In Exercises 111121, solve each inequality. Other than , useinterva...
 1.114: In Exercises 111121, solve each inequality. Other than , useinterva...
 1.115: In Exercises 111121, solve each inequality. Other than , useinterva...
 1.116: In Exercises 111121, solve each inequality. Other than , useinterva...
 1.117: In Exercises 111121, solve each inequality. Other than , useinterva...
 1.118: In Exercises 111121, solve each inequality. Other than , useinterva...
 1.119: In Exercises 111121, solve each inequality. Other than , useinterva...
 1.120: In Exercises 111121, solve each inequality. Other than , useinterva...
 1.121: In Exercises 111121, solve each inequality. Other than , useinterva...
 1.122: In Exercises 122123, use interval notation to represent all valueso...
 1.123: In Exercises 122123, use interval notation to represent all valueso...
 1.124: A car rental agency rents a certain car for $40 per day withunlimit...
 1.125: To receive a B in a course, you must have an average of atleast 80%...
 1.126: A retiree requires an annual income of at least $9000from an invest...
Solutions for Chapter 1: Equations and Inequalities
Full solutions for College Algebra  7th Edition
ISBN: 9780134469164
Solutions for Chapter 1: Equations and Inequalities
Get Full SolutionsSince 126 problems in chapter 1: Equations and Inequalities have been answered, more than 32479 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: College Algebra , edition: 7. College Algebra was written by and is associated to the ISBN: 9780134469164. Chapter 1: Equations and Inequalities includes 126 full stepbystep solutions.

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

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.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

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

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

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

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.