 1.6.1: 2 =
 1.6.2: True or False x 0 for any real number x.
 1.6.3: The solution set of the equation is
 1.6.4: The solution set of the inequality is {x
 1.6.5: True or False The equation has no solution
 1.6.6: True or False The inequality has the set of real numbers as its sol...
 1.6.7: In 734, solve each equation. 2x = 6
 1.6.8: In 734, solve each equation. 3x = 12
 1.6.9: In 734, solve each equation. 2x + 3 = 5
 1.6.10: In 734, solve each equation. 3x  1 = 2
 1.6.11: In 734, solve each equation. 1  4t + 8 = 13
 1.6.12: In 734, solve each equation. 1  2z + 6 = 9
 1.6.13: In 734, solve each equation. 2x = 8
 1.6.14: In 734, solve each equation. x = 1
 1.6.15: In 734, solve each equation. 2x = 4
 1.6.16: In 734, solve each equation. 3x = 9
 1.6.17: In 734, solve each equation. 23 x = 9
 1.6.18: In 734, solve each equation. 34 x = 9
 1.6.19: In 734, solve each equation. `x3+25 ` = 2
 1.6.20: In 734, solve each equation. `x2  13 ` = 1
 1.6.21: In 734, solve each equation. u  2 =  12
 1.6.22: In 734, solve each equation. 2  v = 1
 1.6.23: In 734, solve each equation. 4  2x = 3
 1.6.24: In 734, solve each equation. 5  `12x ` = 3
 1.6.25: In 734, solve each equation. x2  9 = 0
 1.6.26: In 734, solve each equation. x2  16 = 0
 1.6.27: In 734, solve each equation. x2  2x = 3
 1.6.28: In 734, solve each equation. x2 + x = 12
 1.6.29: In 734, solve each equation. x2 + x  1 = 1
 1.6.30: In 734, solve each equation. x2 + 3x  2 = 2
 1.6.31: In 734, solve each equation. `3x  22x  3 ` = 2
 1.6.32: In 734, solve each equation. `2x + 13x + 4 ` = 1
 1.6.33: In 734, solve each equation. x2 + 3x = x2  2x
 1.6.34: In 734, solve each equation. x2  2x = x2 + 6x
 1.6.35: In 3562, solve each inequality. Express your answer using set notat...
 1.6.36: In 3562, solve each inequality. Express your answer using set notat...
 1.6.37: In 3562, solve each inequality. Express your answer using set notat...
 1.6.38: In 3562, solve each inequality. Express your answer using set notat...
 1.6.39: In 3562, solve each inequality. Express your answer using set notat...
 1.6.40: In 3562, solve each inequality. Express your answer using set notat...
 1.6.41: In 3562, solve each inequality. Express your answer using set notat...
 1.6.42: In 3562, solve each inequality. Express your answer using set notat...
 1.6.43: In 3562, solve each inequality. Express your answer using set notat...
 1.6.44: In 3562, solve each inequality. Express your answer using set notat...
 1.6.45: In 3562, solve each inequality. Express your answer using set notat...
 1.6.46: In 3562, solve each inequality. Express your answer using set notat...
 1.6.47: In 3562, solve each inequality. Express your answer using set notat...
 1.6.48: In 3562, solve each inequality. Express your answer using set notat...
 1.6.49: In 3562, solve each inequality. Express your answer using set notat...
 1.6.50: In 3562, solve each inequality. Express your answer using set notat...
 1.6.51: In 3562, solve each inequality. Express your answer using set notat...
 1.6.52: In 3562, solve each inequality. Express your answer using set notat...
 1.6.53: In 3562, solve each inequality. Express your answer using set notat...
 1.6.54: In 3562, solve each inequality. Express your answer using set notat...
 1.6.55: In 3562, solve each inequality. Express your answer using set notat...
 1.6.56: In 3562, solve each inequality. Express your answer using set notat...
 1.6.57: In 3562, solve each inequality. Express your answer using set notat...
 1.6.58: In 3562, solve each inequality. Express your answer using set notat...
 1.6.59: In 3562, solve each inequality. Express your answer using set notat...
 1.6.60: In 3562, solve each inequality. Express your answer using set notat...
 1.6.61: In 3562, solve each inequality. Express your answer using set notat...
 1.6.62: In 3562, solve each inequality. Express your answer using set notat...
 1.6.63: Body Temperature Normal human body temperature is 98.6F. If a tempe...
 1.6.64: Household Voltage In the United States, normal household voltage is...
 1.6.65: Reading Books A Gallup poll conducted May 2022, 2005, found that Am...
 1.6.66: Speed of Sound According to data from the Hill Aerospace Museum (Hi...
 1.6.67: Express the fact that x differs from 3 by less than as an inequalit...
 1.6.68: Express the fact that x differs from by less than 1 as an inequalit...
 1.6.69: Express the fact that x differs from by more than 2 as an inequalit...
 1.6.70: Express the fact that x differs from 2 by more than 3 as an inequal...
 1.6.71: In 7176, find a and b. If then a 6 x + 4 6 b.
 1.6.72: In 7176, find a and b. If then a 6 x  2 6 b
 1.6.73: In 7176, find a and b. If then a 2x  3 b.
 1.6.74: In 7176, find a and b. If then a 3x + 1 b
 1.6.75: In 7176, find a and b. If then a 1x  10 x  2 7, b.
 1.6.76: In 7176, find a and b. If then x + 1 3, b.
 1.6.77: Show that: if and , then [Hint: .]
 1.6.78: Show that a a.
 1.6.79: Prove the triangle inequality [Hint: Expand and use the result of 78.]
 1.6.80: Prove that[Hint: Apply the triangle inequality from to]
 1.6.81: If show that the solution set of the inequality consists of all num...
 1.6.82: If show that the solution set of the inequality consists of all num...
 1.6.83: In 8390, use the results found in 81 and 82 to solve each inequalit...
 1.6.84: In 8390, use the results found in 81 and 82 to solve each inequalit...
 1.6.85: In 8390, use the results found in 81 and 82 to solve each inequalit...
 1.6.86: In 8390, use the results found in 81 and 82 to solve each inequalit...
 1.6.87: In 8390, use the results found in 81 and 82 to solve each inequalit...
 1.6.88: In 8390, use the results found in 81 and 82 to solve each inequalit...
 1.6.89: In 8390, use the results found in 81 and 82 to solve each inequalit...
 1.6.90: In 8390, use the results found in 81 and 82 to solve each inequalit...
 1.6.91: Solve 3x  2x + 1 = 4.
 1.6.92: Solve x + 3x  2 = 2.
 1.6.93: The equation has no solution. Explain why.
 1.6.94: The inequality has all real numbers as solutions. Explain why
 1.6.95: The inequality has as solution set Explain why.
Solutions for Chapter 1.6: Equations and Inequalities Involving Absolute Value
Full solutions for College Algebra  9th Edition
ISBN: 9780321716811
Solutions for Chapter 1.6: Equations and Inequalities Involving Absolute Value
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 95 problems in chapter 1.6: Equations and Inequalities Involving Absolute Value have been answered, more than 37319 students have viewed full stepbystep solutions from this chapter. College Algebra was written by and is associated to the ISBN: 9780321716811. Chapter 1.6: Equations and Inequalities Involving Absolute Value includes 95 full stepbystep solutions. This textbook survival guide was created for the textbook: College Algebra, edition: 9.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

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.

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

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.

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

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

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

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

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

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

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