 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 9755 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!

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

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

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

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

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Iterative method.
A sequence of steps intended to approach the desired solution.

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

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

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.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).
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