 1.6.1: Solve each inequality. Graph the solution set on a number line.
 1.6.2: Solve each inequality. Graph the solution set on a number line.
 1.6.3: Solve each inequality. Graph the solution set on a number line.
 1.6.4: Solve each inequality. Graph the solution set on a number line.
 1.6.5: Solve each inequality. Graph the solution set on a number line.
 1.6.6: Solve each inequality. Graph the solution set on a number line.
 1.6.7: Solve each inequality. Graph the solution set on a number line.
 1.6.8: Solve each inequality. Graph the solution set on a number line.
 1.6.9: Solve each inequality. Graph the solution set on a number line.
 1.6.10: Solve each inequality. Graph the solution set on a number line.
 1.6.11: Deion is considering several types of flooring for his kitchen. He ...
 1.6.12: Solve each inequality. Graph the solution set on a number line.
 1.6.13: Solve each inequality. Graph the solution set on a number line.
 1.6.14: Solve each inequality. Graph the solution set on a number line.
 1.6.15: Solve each inequality. Graph the solution set on a number line.
 1.6.16: Solve each inequality. Graph the solution set on a number line.
 1.6.17: Solve each inequality. Graph the solution set on a number line.
 1.6.18: Solve each inequality. Graph the solution set on a number line.
 1.6.19: Solve each inequality. Graph the solution set on a number line.
 1.6.20: Solve each inequality. Graph the solution set on a number line.
 1.6.21: Solve each inequality. Graph the solution set on a number line.
 1.6.22: Write an inequality to represent the allowable speed for a car on a...
 1.6.23: Write an inequality to represent the speed at which a tractortrail...
 1.6.24: Solve each inequality. Graph the solution set on a number line
 1.6.25: Solve each inequality. Graph the solution set on a number line
 1.6.26: Solve each inequality. Graph the solution set on a number line
 1.6.27: Solve each inequality. Graph the solution set on a number line
 1.6.28: Solve each inequality. Graph the solution set on a number line
 1.6.29: Solve each inequality. Graph the solution set on a number line
 1.6.30: Solve each inequality. Graph the solution set on a number line
 1.6.31: Solve each inequality. Graph the solution set on a number line
 1.6.32: A Siamese Fighting Fish, better known as a Betta fish, is one of th...
 1.6.33: Write an absolute value inequality for each graph
 1.6.34: Write an absolute value inequality for each graph
 1.6.35: Write an absolute value inequality for each graph
 1.6.36: Write an absolute value inequality for each graph
 1.6.37: Write an absolute value inequality for each graph
 1.6.38: Write an absolute value inequality for each graph
 1.6.39: Hypothermia and hyperthermia are similar words but have opposite me...
 1.6.40: Write a compound inequality to describe this situation.
 1.6.41: If the distance around the thickest part of a package you want to m...
 1.6.42: Suppose a certain template is 24.42 inches long. Use the informatio...
 1.6.43: Find the acceptable lengths for that part of a car if the template ...
 1.6.44: Write three inequalities to express the relationships among the sid...
 1.6.45: Write a compound inequality to describe the range of possible measu...
 1.6.46: Clear the Y= list. Enter (5x + 2 > 12) and (3x  8 < 1) as Y1. With...
 1.6.47: Using the TRACE function, investigate the graph. Based on your inve...
 1.6.48: Write the expression you would enter for Y1 to find the solution se...
 1.6.49: A graphing calculator can also be used to solve absolute value ineq...
 1.6.50: Write a compound inequality for which the graph is the empty set
 1.6.51: Sabrina and Isaac are solving 3x + 7 > 2. Who is correct? Explain y...
 1.6.52: Graph each set on a number line. a. 2 < x < 4 b. x < 1 or x > 3 c...
 1.6.53: Use the information about fasting on page 41 to explain how compoun...
 1.6.54: If 5 < a < 7 < b < 14, then which of the following best describes _...
 1.6.55: If 5 < a < 7 < b < 14, then which of the following best describes _...
 1.6.56: Solve each inequality. Then graph the solution set on a number line.
 1.6.57: Solve each inequality. Then graph the solution set on a number line.
 1.6.58: Solve each inequality. Then graph the solution set on a number line.
 1.6.59: To get a chance to win a car, you must guess the number of keys in ...
 1.6.60: Solve each equation. Check your solutions.
 1.6.61: Solve each equation. Check your solutions.
 1.6.62: Solve each equation. Check your solutions.
 1.6.63: Name the property illustrated by each statement.
 1.6.64: Name the property illustrated by each statement.
 1.6.65: Name the property illustrated by each statement.
 1.6.66: Illustrate the Distributive Property by writing two expressions to ...
 1.6.67: Evaluate the expressions from Exercise 66.
 1.6.68: Simplify each expression
 1.6.69: Simplify each expression
 1.6.70: Simplify each expression
 1.6.71: Simplify each expression
 1.6.72: Simplify each expression
Solutions for Chapter 1.6: Solving Compound and Absolute Value Inequalities
Full solutions for California Algebra 2: Concepts, Skills, and Problem Solving  1st Edition
ISBN: 9780078778568
Solutions for Chapter 1.6: Solving Compound and Absolute Value Inequalities
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 72 problems in chapter 1.6: Solving Compound and Absolute Value Inequalities have been answered, more than 41794 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: California Algebra 2: Concepts, Skills, and Problem Solving, edition: 1. Chapter 1.6: Solving Compound and Absolute Value Inequalities includes 72 full stepbystep solutions. California Algebra 2: Concepts, Skills, and Problem Solving was written by and is associated to the ISBN: 9780078778568.

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

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!

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

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).

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

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

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

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.

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

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

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

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.