 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 29953 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.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

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.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

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].

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

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].

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

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

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

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

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.

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

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

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.