 2.8.1: Concept Check Work each problem.When graphing an inequality, use a ...
 2.8.2: Concept Check Work each problem.True or false? In interval notation...
 2.8.3: Concept Check Work each problem.In interval notation, the set is wr...
 2.8.4: Concept Check Work each problem.How does the graph of differ from t...
 2.8.5: Concept Check Write an inequality involving the variable x that des...
 2.8.6: Concept Check Write an inequality involving the variable x that des...
 2.8.7: Concept Check Write an inequality involving the variable x that des...
 2.8.8: Concept Check Write an inequality involving the variable x that des...
 2.8.9: Write each inequality in interval notation, and graph the interval....
 2.8.10: Write each inequality in interval notation, and graph the interval....
 2.8.11: Write each inequality in interval notation, and graph the interval....
 2.8.12: Write each inequality in interval notation, and graph the interval....
 2.8.13: Write each inequality in interval notation, and graph the interval....
 2.8.14: Write each inequality in interval notation, and graph the interval....
 2.8.15: Write each inequality in interval notation, and graph the interval....
 2.8.16: Write each inequality in interval notation, and graph the interval....
 2.8.17: Write each inequality in interval notation, and graph the interval....
 2.8.18: Write each inequality in interval notation, and graph the interval....
 2.8.19: Solve each inequality. Write the solution set in interval notation,...
 2.8.20: Solve each inequality. Write the solution set in interval notation,...
 2.8.21: Solve each inequality. Write the solution set in interval notation,...
 2.8.22: Solve each inequality. Write the solution set in interval notation,...
 2.8.23: Solve each inequality. Write the solution set in interval notation,...
 2.8.24: Solve each inequality. Write the solution set in interval notation,...
 2.8.25: Under what conditions must the inequality symbol be reversed when s...
 2.8.26: Concept Check If p 6 q and r 6 0 , which one of the following state...
 2.8.27: Solve each inequality. Write the solution set in interval notation,...
 2.8.28: Solve each inequality. Write the solution set in interval notation,...
 2.8.29: Solve each inequality. Write the solution set in interval notation,...
 2.8.30: Solve each inequality. Write the solution set in interval notation,...
 2.8.31: Solve each inequality. Write the solution set in interval notation,...
 2.8.32: Solve each inequality. Write the solution set in interval notation,...
 2.8.33: Solve each inequality. Write the solution set in interval notation,...
 2.8.34: Solve each inequality. Write the solution set in interval notation,...
 2.8.35: Solve each inequality. Write the solution set in interval notation,...
 2.8.36: Solve each inequality. Write the solution set in interval notation,...
 2.8.37: Solve each inequality. Write the solution set in interval notation,...
 2.8.38: Solve each inequality. Write the solution set in interval notation,...
 2.8.39: Solve each inequality. Write the solution set in interval notation,...
 2.8.40: Solve each inequality. Write the solution set in interval notation,...
 2.8.41: Solve each inequality. Write the solution set in interval notation,...
 2.8.42: Solve each inequality. Write the solution set in interval notation,...
 2.8.43: Solve each inequality. Write the solution set in interval notation,...
 2.8.44: Solve each inequality. Write the solution set in interval notation,...
 2.8.45: Solve each inequality. Write the solution set in interval notation,...
 2.8.46: Solve each inequality. Write the solution set in interval notation,...
 2.8.47: Solve each inequality. Write the solution set in interval notation,...
 2.8.48: Solve each inequality. Write the solution set in interval notation,...
 2.8.49: Solve each inequality. Write the solution set in interval notation,...
 2.8.50: Solve each inequality. Write the solution set in interval notation,...
 2.8.51: Solve each inequality. Write the solution set in interval notation,...
 2.8.52: Solve each inequality. Write the solution set in interval notation,...
 2.8.53: Solve each inequality. Write the solution set in interval notation,...
 2.8.54: Solve each inequality. Write the solution set in interval notation,...
 2.8.55: Solve each inequality. Write the solution set in interval notation,...
 2.8.56: Solve each inequality. Write the solution set in interval notation,...
 2.8.57: Solve each inequality. Write the solution set in interval notation,...
 2.8.58: Solve each inequality. Write the solution set in interval notation,...
 2.8.59: Work Exercises 5962 in order, to see how the solutions of an inequa...
 2.8.60: Work Exercises 5962 in order, to see how the solutions of an inequa...
 2.8.61: Work Exercises 5962 in order, to see how the solutions of an inequa...
 2.8.62: Work Exercises 5962 in order, to see how the solutions of an inequa...
 2.8.63: Concept Check Translate each statement into an inequality. Use x as...
 2.8.64: Concept Check Translate each statement into an inequality. Use x as...
 2.8.65: Concept Check Translate each statement into an inequality. Use x as...
 2.8.66: Concept Check Translate each statement into an inequality. Use x as...
 2.8.67: Concept Check Translate each statement into an inequality. Use x as...
 2.8.68: Concept Check Translate each statement into an inequality. Use x as...
 2.8.69: Solve each problem. See Example 6.Christy Heinrich has scores of 76...
 2.8.70: Solve each problem. See Example 6.Joseph Despagne has scores of 96 ...
 2.8.71: Solve each problem. See Example 6.When 2 is added to the difference...
 2.8.72: Solve each problem. See Example 6.When 8 is subtracted from the sum...
 2.8.73: Solve each problem. See Example 6.The formula for converting Fahren...
 2.8.74: Solve each problem. See Example 6.The formula for converting Celsiu...
 2.8.75: Solve each problem. See Example 6.For what values of x would the re...
 2.8.76: Solve each problem. See Example 6.For what values of x would the tr...
 2.8.77: Solve each problem. See Example 6.For a certain provider, an intern...
 2.8.78: Solve each problem. See Example 6.At the Speedy Gasn Go, a car wash...
 2.8.79: A company that produces DVDs has found that revenue from the sales ...
 2.8.80: A company that produces DVDs has found that revenue from the sales ...
 2.8.81: A company that produces DVDs has found that revenue from the sales ...
 2.8.82: A company that produces DVDs has found that revenue from the sales ...
 2.8.83: Concept Check Write a threepart inequality involving the variable ...
 2.8.84: Concept Check Write a threepart inequality involving the variable ...
 2.8.85: Concept Check Write a threepart inequality involving the variable ...
 2.8.86: Concept Check Write a threepart inequality involving the variable ...
 2.8.87: Write each inequality in interval notation, and graph the interval....
 2.8.88: Write each inequality in interval notation, and graph the interval....
 2.8.89: Write each inequality in interval notation, and graph the interval....
 2.8.90: Write each inequality in interval notation, and graph the interval....
 2.8.91: Write each inequality in interval notation, and graph the interval....
 2.8.92: Write each inequality in interval notation, and graph the interval....
 2.8.93: Solve each inequality. Write the solution set in interval notation,...
 2.8.94: Solve each inequality. Write the solution set in interval notation,...
 2.8.95: Solve each inequality. Write the solution set in interval notation,...
 2.8.96: Solve each inequality. Write the solution set in interval notation,...
 2.8.97: Solve each inequality. Write the solution set in interval notation,...
 2.8.98: Solve each inequality. Write the solution set in interval notation,...
 2.8.99: Solve each inequality. Write the solution set in interval notation,...
 2.8.100: Solve each inequality. Write the solution set in interval notation,...
 2.8.101: Solve each inequality. Write the solution set in interval notation,...
 2.8.102: Solve each inequality. Write the solution set in interval notation,...
 2.8.103: Solve each inequality. Write the solution set in interval notation,...
 2.8.104: Solve each inequality. Write the solution set in interval notation,...
 2.8.105: Find the value of y when (a) x = 2 and (b) x = 4. See Sections 1.3...
 2.8.106: Find the value of y when (a) x = 2 and (b) x = 4. See Sections 1.3...
 2.8.107: Find the value of y when (a) x = 2 and (b) x = 4. See Sections 1.3...
 2.8.108: Find the value of y when (a) x = 2 and (b) x = 4. See Sections 1.3...
 2.8.109: Find the value of y when (a) x = 2 and (b) x = 4. See Sections 1.3...
 2.8.110: Find the value of y when (a) x = 2 and (b) x = 4. See Sections 1.3...
Solutions for Chapter 2.8: Solving Linear Inequalities
Full solutions for Beginning Algebra  11th Edition
ISBN: 9780321673480
Solutions for Chapter 2.8: Solving Linear Inequalities
Get Full SolutionsThis textbook survival guide was created for the textbook: Beginning Algebra, edition: 11. Beginning Algebra was written by and is associated to the ISBN: 9780321673480. Chapter 2.8: Solving Linear Inequalities includes 110 full stepbystep solutions. Since 110 problems in chapter 2.8: Solving Linear Inequalities have been answered, more than 36078 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

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).

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!

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

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.

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

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

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

Outer product uv T
= column times row = rank one matrix.

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

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.

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

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

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