 4.2.1: The set of elements common to both set A and set B is called the of...
 4.2.2: The set of elements that are members of set A or set B or of both s...
 4.2.3: The set of elements common to both (, 9) and (, 12) is .
 4.2.4: The set of elements in (, 9) or (, 12) or in both sets is .
 4.2.5: The way to solve 7 6 3x  4 5 is to isolate x in the .
 4.2.6: {w, y, z}
 4.2.7: x 7 3 and x 7 6
 4.2.8: x 7 2 and x 7 4
 4.2.9: x 5 and x 1
 4.2.10: x 6 and x 2
 4.2.11: x 6 2 and x 1
 4.2.12: x 6 3 and x 1
 4.2.13: x 7 2 and x 6 1
 4.2.14: x 7 3 and x 6 1
 4.2.15: 5x 6 20 and 3x 7 18
 4.2.16: 3x 15 and 2x 7 6
 4.2.17: x  4 2 and 3x + 1 7 8
 4.2.18: 3x + 2 7 4 and 2x  1 6 5
 4.2.19: 2x 7 5x  15 and 7x 7 2x + 10
 4.2.20: 6  5x 7 1  3x and 4x  3 7 x  9
 4.2.21: 4(1  x) 6 6 and x  7 5 2
 4.2.22: 5(x  2) 7 15 and x  6 4 2
 4.2.23: x  1 7x  1 and 4x  7 6 3  x
 4.2.24: 2x + 1 7 4x  3 and x  1 3x + 5
 4.2.25: 6 6 x + 3 6 8
 4.2.26: 7 6 x + 5 6 1
 4.2.27: 3 x  2 6 1
 4.2.28: 6 6 x  4 1
 4.2.29: 11 6 2x  1 5
 4.2.30: 3 4x  3 6 19
 4.2.31: 3 2x 3  5 6 1
 4.2.32: 6 x 2  4 6 3
 4.2.33: {1, 2, 3, 4} {2, 4, 5}
 4.2.34: {1, 3, 7, 8} {2, 3, 8}
 4.2.35: {1, 3, 5, 7} {2, 4, 6, 8, 10}
 4.2.36: {0, 1, 3, 5} {2, 4, 6}
 4.2.37: {a, e, i, o, u}
 4.2.38: {e, m, p, t, y}
 4.2.39: x 7 3 or x 7 6
 4.2.40: x 7 2 or x 7 4
 4.2.41: x 5 or x 1
 4.2.42: x 6 or x 2
 4.2.43: x 6 2 or x 1
 4.2.44: x 6 3 or x 1
 4.2.45: x 2 or x 6 1
 4.2.46: x 3 or x 6 1
 4.2.47: 3x 7 12 or 2x 6 6
 4.2.48: 3x 6 3 or 2x 7 10
 4.2.49: 3x + 2 5 or 5x  7 8
 4.2.50: 2x  5 11 or 5x + 1 6
 4.2.51: 4x + 3 6 1 or 2x  3 11
 4.2.52: 2x + 1 6 15 or 3x  4 1
 4.2.53: 2x + 5 7 7 or 3x + 10 7 2x
 4.2.54: 16  3x 8 or 13  x 7 4x + 3
 4.2.55: Let f(x) = 2x + 3 and g(x) = 3x  1. Find all values of x for which...
 4.2.56: Let f(x) = 4x + 5 and g(x) = 3x  4. Find all values of x for which...
 4.2.57: Let f(x) = 3x  1 and g(x) = 4  x. Find all values of x for which ...
 4.2.58: Let f(x) = 2x  5 and g(x) = 3  x. Find all values of x for which ...
 4.2.59: c 6 ax  b 6 c
 4.2.60: 2 6 ax  b c 6 2
 4.2.61: 3 2x  1 5
 4.2.62: x  2 6 2x  1 6 x + 2
 4.2.63: Solve x  2 6 2x  1 6 x + 2, the inequality in Exercise 62, using ...
 4.2.64: Use the hint given in Exercise 63 to solve x 3x  10 2x.
 4.2.65: 2 5x + 3 6 13
 4.2.66: 3 6 2x  5 3
 4.2.67: 5  4x 1 and 3  7x 6 31
 4.2.68: 5 6 3x + 4 16
 4.2.69: a. In which years will more than 33% of U.S. households have an int...
 4.2.70: a. In which years will more than 34% of U.S. households have an int...
 4.2.71: A basic cellphone plan costs $20 per month for 60 calling minutes. ...
 4.2.72: The formula for converting Fahrenheit temperature, F, to Celsius te...
 4.2.73: On the first four exams, your grades are 70, 75, 87, and 92. There ...
 4.2.74: On the first four exams, your grades are 82, 75, 80, and 90. There ...
 4.2.75: The toll to a bridge is $3.00. A threemonth pass costs $7.50 and r...
 4.2.76: Parts for an automobile repair cost $175. The mechanic charges $34 ...
 4.2.77: Describe what is meant by the intersection of two sets. Give an exa...
 4.2.78: Explain how to solve a compound inequality involving and.
 4.2.79: Why is 1 6 2x + 3 6 9 a compound inequality? What are the two inequ...
 4.2.80: Explain how to solve 1 6 2x + 3 6 9.
 4.2.81: Describe what is meant by the union of two sets. Give an example.
 4.2.82: Explain how to solve a compound inequality involving or.
 4.2.83: 1 6 x + 3 6 9
 4.2.84: 1 6 x + 4 2 6 3
 4.2.85: 1 4x  7 3
 4.2.86: 2 4  x 7
 4.2.87: Use a graphing utilitys TABLE feature to verify your work in Exerci...
 4.2.88: Ive noticed that when solving some compound inequalities with or, t...
 4.2.89: Compound inequalities with and have solutions that satisfy both ine...
 4.2.90: Im considering the compound inequality x 6 8 and x 8, so the soluti...
 4.2.91: Im considering the compound inequality x 6 8 or x 8, so the solutio...
 4.2.92: ( , 1] [4, ) = [4, 1]
 4.2.93: ( , 3) ( , 2) = ( , 2)
 4.2.94: The union of two sets can never give the same result as the interse...
 4.2.95: The solution set of the compound inequality x 6 a and x 7 a is the ...
 4.2.96: Solve and express the solution set in interval notation: 7 8  3x ...
 4.2.97: The domain of f
 4.2.98: The domain of g
 4.2.99: The domain of f + g
 4.2.100: The domain of f g
 4.2.101: At the end of the day, the change machine at a laundrette contained...
 4.2.102: If f(x) = x2  3x + 4 and g(x) = 2x  5, find (g  f)(x) and (g  f...
 4.2.103: Use function notation to write the equation of the line passing thr...
 4.2.104: Simplify: 4  [2(x  4)  5]. (Section 1.2, Example 14)
 4.2.105: Find all values of x satisfying 1  4x = 3 or 1  4x = 3.
 4.2.106: Find all values of x satisfying 3x  1 = x + 5 or 3x  1 = (x + 5).
 4.2.107: a. Substitute 5 for x and determine whether 5 satisfies 2x + 3 5....
Solutions for Chapter 4.2: Compound Inequalities
Full solutions for Intermediate Algebra for College Students  6th Edition
ISBN: 9780321758934
Solutions for Chapter 4.2: Compound Inequalities
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 4.2: Compound Inequalities includes 107 full stepbystep solutions. Intermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758934. Since 107 problems in chapter 4.2: Compound Inequalities have been answered, more than 74669 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.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

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).

Column space C (A) =
space of all combinations of the columns of A.

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

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.

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

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.

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.

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

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

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!

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

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

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

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