 Chapter 4.1: 6x + 3 15
 Chapter 4.2: 6x  9 4x  3
 Chapter 4.3: x 3  3 4  1 7 x 2
 Chapter 4.4: 6x + 5 7 2(x  3)  25
 Chapter 4.5: 3(2x  1)  2(x  4) 7 + 2(3 + 4x)
 Chapter 4.6: 2x + 7 5x  6  3x
 Chapter 4.7: A person can choose between two charges on a checking account. The ...
 Chapter 4.8: A salesperson earns $500 per month plus a commission of 20% of sale...
 Chapter 4.9: A B
 Chapter 4.10: A C
 Chapter 4.11: A B
 Chapter 4.12: A C
 Chapter 4.13: x 3 and x 6 6
 Chapter 4.14: x 3 or x 6 6
 Chapter 4.15: 2x 6 12 and x  3 6 5
 Chapter 4.16: 5x + 3 18 and 2x  7 5
 Chapter 4.17: 2x  5 7 1 and 3x 6 3
 Chapter 4.18: 2x  5 7 1 or 3x 6 3
 Chapter 4.19: x + 1 3 or 4x + 3 6 5
 Chapter 4.20: 5x  2 22 or 3x  2 7 4
 Chapter 4.21: 5x + 4 11 or 1  4x 9
 Chapter 4.22: 3 6 x + 2 4
 Chapter 4.23: 1 4x + 2 6
 Chapter 4.24: To receive a B in a course, you must have an average of at least 80...
 Chapter 4.25: 2x + 1 = 7
 Chapter 4.26: 3x + 2 = 5
 Chapter 4.27: 2 x  3  7 = 10
 Chapter 4.28: 4x  3 = 7x + 9
 Chapter 4.29: 2x + 3 15
 Chapter 4.30: 2x + 6 3 ` 7 2
 Chapter 4.31: 2x + 5  7 6 6
 Chapter 4.32: 4 x + 2 + 5 7
 Chapter 4.33: 2x  3 + 4 10
 Chapter 4.34: Approximately 90% of the population sleeps h hours daily, where h i...
 Chapter 4.35: 3x  4y 7 12
 Chapter 4.36: x  3y 6
 Chapter 4.37: y  1 2 x + 2
 Chapter 4.38: y 7 3 5 x
 Chapter 4.39: x 2
 Chapter 4.40: y 7 3
 Chapter 4.41: e 2x  y 4 x + y 5
 Chapter 4.42: e y 6 x + 4 y 7 x  4
 Chapter 4.43: 3 x 6 5
 Chapter 4.44: 2 6 y 6
 Chapter 4.45: e x 3 y 0
 Chapter 4.46: e 2x  y 7 4 x 0
 Chapter 4.47: e x + y 6 y 2x  3
 Chapter 4.48: 3x + 2y 4 x  y 3 x 0, y 0
 Chapter 4.49: e 2x  y 7 2 2x  y 6 2
 Chapter 4.50: Find the value of the objective function z = 2x + 3y at each corner...
 Chapter 4.51: Objective Function Constraints z = 2x + 3y x 0, y 0 x + y 8 3x + 2y 6
 Chapter 4.52: Objective Function Constraints z = x + 4y e 0 x 5, 0 y 7 x + y 3
 Chapter 4.53: Objective Function Constraints z = 5x + 6yx 0, y 0y x2x + y 122x + ...
 Chapter 4.54: A paper manufacturing company converts wood pulp to writing paper a...
 Chapter 4.55: A manufacturer of lightweight tents makes two models whose specific...
Solutions for Chapter Chapter 4: Inequalities and Problem Solving
Full solutions for Intermediate Algebra for College Students  6th Edition
ISBN: 9780321758934
Solutions for Chapter Chapter 4: Inequalities and Problem Solving
Get Full SolutionsIntermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758934. Since 55 problems in chapter Chapter 4: Inequalities and Problem Solving have been answered, more than 29748 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Intermediate Algebra for College Students, edition: 6. Chapter Chapter 4: Inequalities and Problem Solving includes 55 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions.

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!

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.

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

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

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

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 .

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

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.

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.

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.