 1.7.1: Fill in the blanks. The set of all real numbers that are solutions ...
 1.7.2: Fill in the blanks. The set of all points on the real number line t...
 1.7.3: Fill in the blanks. To solve a linear inequality in one variable, y...
 1.7.4: Fill in the blanks. Two inequalities that have the same solution se...
 1.7.5: Fill in the blanks. It is sometimes possible to write two inequalit...
 1.7.6: Fill in the blanks. The symbol is called a ________ symbol and is u...
 1.7.7: In Exercises 714, (a) write an inequality that represents the inter...
 1.7.8: In Exercises 714, (a) write an inequality that represents the inter...
 1.7.9: In Exercises 714, (a) write an inequality that represents the inter...
 1.7.10: In Exercises 714, (a) write an inequality that represents the inter...
 1.7.11: In Exercises 714, (a) write an inequality that represents the inter...
 1.7.12: In Exercises 714, (a) write an inequality that represents the inter...
 1.7.13: In Exercises 714, (a) write an inequality that represents the inter...
 1.7.14: In Exercises 714, (a) write an inequality that represents the inter...
 1.7.15: In Exercises 1522, match the inequality with its graph. [The graphs...
 1.7.16: In Exercises 1522, match the inequality with its graph. [The graphs...
 1.7.17: In Exercises 1522, match the inequality with its graph. [The graphs...
 1.7.18: In Exercises 1522, match the inequality with its graph. [The graphs...
 1.7.19: In Exercises 1522, match the inequality with its graph. [The graphs...
 1.7.20: In Exercises 1522, match the inequality with its graph. [The graphs...
 1.7.21: In Exercises 1522, match the inequality with its graph. [The graphs...
 1.7.22: In Exercises 1522, match the inequality with its graph. [The graphs...
 1.7.23: In Exercises 2328, determine whether each value of is a solution of...
 1.7.24: In Exercises 2328, determine whether each value of is a solution of...
 1.7.25: In Exercises 2328, determine whether each value of is a solution of...
 1.7.26: In Exercises 2328, determine whether each value of is a solution of...
 1.7.27: In Exercises 2328, determine whether each value of is a solution of...
 1.7.28: In Exercises 2328, determine whether each value of is a solution of...
 1.7.29: In Exercises 2956, solve the inequality and sketch the solution on ...
 1.7.30: In Exercises 2956, solve the inequality and sketch the solution on ...
 1.7.31: In Exercises 2956, solve the inequality and sketch the solution on ...
 1.7.32: In Exercises 2956, solve the inequality and sketch the solution on ...
 1.7.33: In Exercises 2956, solve the inequality and sketch the solution on ...
 1.7.34: In Exercises 2956, solve the inequality and sketch the solution on ...
 1.7.35: In Exercises 2956, solve the inequality and sketch the solution on ...
 1.7.36: In Exercises 2956, solve the inequality and sketch the solution on ...
 1.7.37: In Exercises 2956, solve the inequality and sketch the solution on ...
 1.7.38: In Exercises 2956, solve the inequality and sketch the solution on ...
 1.7.39: In Exercises 2956, solve the inequality and sketch the solution on ...
 1.7.40: In Exercises 2956, solve the inequality and sketch the solution on ...
 1.7.41: In Exercises 2956, solve the inequality and sketch the solution on ...
 1.7.42: In Exercises 2956, solve the inequality and sketch the solution on ...
 1.7.43: In Exercises 2956, solve the inequality and sketch the solution on ...
 1.7.44: In Exercises 2956, solve the inequality and sketch the solution on ...
 1.7.45: In Exercises 2956, solve the inequality and sketch the solution on ...
 1.7.46: In Exercises 2956, solve the inequality and sketch the solution on ...
 1.7.47: In Exercises 2956, solve the inequality and sketch the solution on ...
 1.7.48: In Exercises 2956, solve the inequality and sketch the solution on ...
 1.7.49: In Exercises 2956, solve the inequality and sketch the solution on ...
 1.7.50: In Exercises 2956, solve the inequality and sketch the solution on ...
 1.7.51: In Exercises 2956, solve the inequality and sketch the solution on ...
 1.7.52: In Exercises 2956, solve the inequality and sketch the solution on ...
 1.7.53: In Exercises 2956, solve the inequality and sketch the solution on ...
 1.7.54: In Exercises 2956, solve the inequality and sketch the solution on ...
 1.7.55: In Exercises 2956, solve the inequality and sketch the solution on ...
 1.7.56: In Exercises 2956, solve the inequality and sketch the solution on ...
 1.7.57: In Exercises 5772, solve the inequality and sketch the solution on ...
 1.7.58: In Exercises 5772, solve the inequality and sketch the solution on ...
 1.7.59: In Exercises 5772, solve the inequality and sketch the solution on ...
 1.7.60: In Exercises 5772, solve the inequality and sketch the solution on ...
 1.7.61: In Exercises 5772, solve the inequality and sketch the solution on ...
 1.7.62: In Exercises 5772, solve the inequality and sketch the solution on ...
 1.7.63: In Exercises 5772, solve the inequality and sketch the solution on ...
 1.7.64: In Exercises 5772, solve the inequality and sketch the solution on ...
 1.7.65: In Exercises 5772, solve the inequality and sketch the solution on ...
 1.7.66: In Exercises 5772, solve the inequality and sketch the solution on ...
 1.7.67: In Exercises 5772, solve the inequality and sketch the solution on ...
 1.7.68: In Exercises 5772, solve the inequality and sketch the solution on ...
 1.7.69: In Exercises 5772, solve the inequality and sketch the solution on ...
 1.7.70: In Exercises 5772, solve the inequality and sketch the solution on ...
 1.7.71: In Exercises 5772, solve the inequality and sketch the solution on ...
 1.7.72: In Exercises 5772, solve the inequality and sketch the solution on ...
 1.7.73: GRAPHICAL ANALYSIS In Exercises 73 82, use a graphing utility to gr...
 1.7.74: GRAPHICAL ANALYSIS In Exercises 73 82, use a graphing utility to gr...
 1.7.75: GRAPHICAL ANALYSIS In Exercises 73 82, use a graphing utility to gr...
 1.7.76: GRAPHICAL ANALYSIS In Exercises 73 82, use a graphing utility to gr...
 1.7.77: GRAPHICAL ANALYSIS In Exercises 73 82, use a graphing utility to gr...
 1.7.78: GRAPHICAL ANALYSIS In Exercises 73 82, use a graphing utility to gr...
 1.7.79: GRAPHICAL ANALYSIS In Exercises 73 82, use a graphing utility to gr...
 1.7.80: GRAPHICAL ANALYSIS In Exercises 73 82, use a graphing utility to gr...
 1.7.81: GRAPHICAL ANALYSIS In Exercises 73 82, use a graphing utility to gr...
 1.7.82: GRAPHICAL ANALYSIS In Exercises 73 82, use a graphing utility to gr...
 1.7.83: GRAPHICAL ANALYSIS In Exercises 83 88, use a graphing utility to gr...
 1.7.84: GRAPHICAL ANALYSIS In Exercises 83 88, use a graphing utility to gr...
 1.7.85: GRAPHICAL ANALYSIS In Exercises 83 88, use a graphing utility to gr...
 1.7.86: GRAPHICAL ANALYSIS In Exercises 83 88, use a graphing utility to gr...
 1.7.87: GRAPHICAL ANALYSIS In Exercises 83 88, use a graphing utility to gr...
 1.7.88: GRAPHICAL ANALYSIS In Exercises 83 88, use a graphing utility to gr...
 1.7.89: In Exercises 8994, find the interval(s) on the real number line for...
 1.7.90: In Exercises 8994, find the interval(s) on the real number line for...
 1.7.91: In Exercises 8994, find the interval(s) on the real number line for...
 1.7.92: In Exercises 8994, find the interval(s) on the real number line for...
 1.7.93: In Exercises 8994, find the interval(s) on the real number line for...
 1.7.94: In Exercises 8994, find the interval(s) on the real number line for...
 1.7.95: THINK ABOUT IT The graph of can be described as all real numbers wi...
 1.7.96: THINK ABOUT IT The graph of can be described as all real numbers mo...
 1.7.97: In Exercises 97104, use absolute value notation to define the inter...
 1.7.98: In Exercises 97104, use absolute value notation to define the inter...
 1.7.99: In Exercises 97104, use absolute value notation to define the inter...
 1.7.100: In Exercises 97104, use absolute value notation to define the inter...
 1.7.101: All real numbers within 10 units of 12
 1.7.102: All real numbers at least five units from 8
 1.7.103: All real numbers more than four units from
 1.7.104: All real numbers no more than seven units from
 1.7.105: A company expects its earnings per share for the next quarter to be...
 1.7.106: The estimated daily oil production at a refinery is greater than 2 ...
 1.7.107: According to a survey, the percent of U.S. citizens that now conduc...
 1.7.108: The net income of a company is expected to be no less than $239 mil...
 1.7.109: Express as an interval the range of the target heart rate for a 20...
 1.7.110: Express as an interval the range of the target heart rate for a 40...
 1.7.111: JOB OFFERS You are considering two job offers. The first job pays $...
 1.7.112: JOB OFFERS You are considering two job offers. The first job pays $...
 1.7.113: INVESTMENT In order for an investment of $1000 to grow to more than...
 1.7.114: INVESTMENT In order for an investment of $750 to grow to more than ...
 1.7.115: COST, REVENUE, AND PROFIT The revenue from selling units of a produ...
 1.7.116: COST, REVENUE, AND PROFIT The revenue from selling units of a produ...
 1.7.117: DAILY SALES A doughnut shop sells a dozen doughnuts for $4.50. Beyo...
 1.7.118: WEIGHT LOSS PROGRAM A person enrolls in a diet and exercise program...
 1.7.119: DATA ANALYSIS: IQ SCORES AND GPA The admissions office of a college...
 1.7.120: DATA ANALYSIS: WEIGHTLIFTING You want to determine whether there is...
 1.7.121: TEACHERS SALARIES The average salaries (in thousands of dollars) fo...
 1.7.122: EGG PRODUCTION The numbers of eggs (in billions) produced in the Un...
 1.7.123: GEOMETRY The side of a square is measured as 10.4 inches with a pos...
 1.7.124: GEOMETRY The side of a square is measured as 24.2 centimeters with ...
 1.7.125: ACCURACY OF MEASUREMENT You stop at a selfservice gas station to b...
 1.7.126: ACCURACY OF MEASUREMENT You buy six Tbone steaks that cost $14.99 ...
 1.7.127: TIME STUDY A time study was conducted to determine the length of ti...
 1.7.128: HEIGHT The heights of twothirds of the members of a population sat...
 1.7.129: METEOROLOGY An electronic device is to be operated in an environmen...
 1.7.130: MUSIC Michael Kasha of Florida State University used physics and ma...
 1.7.131: TRUE OR FALSE? In Exercises 131 and 132, determine whether the stat...
 1.7.132: TRUE OR FALSE? In Exercises 131 and 132, determine whether the stat...
 1.7.133: Identify the graph of the inequality (a) (b) (c) (d)
 1.7.134: Find sets of values of and such that is a solution of the inequality
 1.7.135: Give an example of an inequality with an unbounded solution set.
 1.7.136: CAPSTONE Describe any differences between properties of equalities ...
Solutions for Chapter 1.7: LINEAR INEQUALITIES IN ONE VARIABLE
Full solutions for College Algebra  8th Edition
ISBN: 9781439048696
Solutions for Chapter 1.7: LINEAR INEQUALITIES IN ONE VARIABLE
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: College Algebra , edition: 8. College Algebra was written by and is associated to the ISBN: 9781439048696. Chapter 1.7: LINEAR INEQUALITIES IN ONE VARIABLE includes 136 full stepbystep solutions. Since 136 problems in chapter 1.7: LINEAR INEQUALITIES IN ONE VARIABLE have been answered, more than 36855 students have viewed full stepbystep solutions from this chapter.

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

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].

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.

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

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

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

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.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

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).

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

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).

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

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!

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

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

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

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

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

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