 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 22850 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.

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).

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.

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

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.

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

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.

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 .

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

Norm
IIA II. The ".e 2 norm" of A is the maximum ratio II Ax II/l1x II = O"max· Then II Ax II < IIAllllxll and IIABII < IIAIIIIBII and IIA + BII < IIAII + IIBII. Frobenius norm IIAII} = L La~. The.e 1 and.e oo norms are largest column and row sums of laij I.

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.

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.

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

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.

Solvable system Ax = b.
The right side b is in the column space of A.

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

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

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