 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 15331 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.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

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

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

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

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 .

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

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.

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

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

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

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.

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

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

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

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