 62.1: Solve each inequality. Check your solution. _t 9 < 12
 62.2: Solve each inequality. Check your solution. 30 > _1 2 n
 62.3: Solve each inequality. Check your solution.  _3 4 r 6
 62.4: Solve each inequality. Check your solution.  _c 8 7
 62.5: Define a variable, write an inequality, and solve each problem. The...
 62.6: Define a variable, write an inequality, and solve each problem. The...
 62.7: FUNDRAISING The Jefferson High School Band Boosters raised more th...
 62.8: Solve each inequality. Check your solution. 7m 42
 62.9: Solve each inequality. Check your solution. 12x > 60
 62.10: Solve each inequality. Check your solution. 75 < 15g
 62.11: Solve each inequality. Check your solution. 21 3s
 62.12: STANDARDIZED TEST PRACTICE The area of the rectangle is less than 8...
 62.13: Solve each inequality. Check your solution. _1 4 m < 17
 62.14: Solve each inequality. Check your solution. _b 10 5
 62.15: Solve each inequality. Check your solution. 7 >  _r 7
 62.16: Solve each inequality. Check your solution.  _a 11> 9
 62.17: Solve each inequality. Check your solution. _5 8 y 15
 62.18: Solve each inequality. Check your solution. 6 > _2 3 v
 62.19: Solve each inequality. Check your solution. 10 _x 2
 62.20: Solve each inequality. Check your solution.  _3 4 q 33
 62.21: Define a variable, write an inequality, and solve each problem. The...
 62.22: Define a variable, write an inequality, and solve each problem. The...
 62.23: Define a variable, write an inequality, and solve each problem. The...
 62.24: Define a variable, write an inequality, and solve each problem. The...
 62.25: Solve each inequality. Check your solution. 6g 144
 62.26: Solve each inequality. Check your solution. 84 < 7t
 62.27: Solve each inequality. Check your solution. 14d 84
 62.28: Solve each inequality. Check your solution. 14n 98
 62.29: Solve each inequality. Check your solution. 32 > 2y
 62.30: Solve each inequality. Check your solution. 64 16z
 62.31: Solve each inequality. Check your solution. 26 < 26s
 62.32: Solve each inequality. Check your solution. 6x > 72
 62.33: For Exercises 33 and 34, define a variable, write an inequality, an...
 62.34: For Exercises 33 and 34, define a variable, write an inequality, an...
 62.35: Solve each inequality. Check your solution.  _2 3 b 9
 62.36: Solve each inequality. Check your solution. 25f 9
 62.37: Solve each inequality. Check your solution. 2.5w < 6.8
 62.38: Solve each inequality. Check your solution. 0.8s > 6.4
 62.39: Solve each inequality. Check your solution. _15c 7 > _3 14
 62.40: Solve each inequality. Check your solution. _4m 5 < _ 3 15
 62.41: Solve  _ m 9 _1 3 . Then graph the solution.
 62.42: Solve _x 4 > _3 16 . Then graph the solution.
 62.43: If 2a 7, then complete each inequality. a. a ____ ? b. 4a ____ ? c...
 62.44: Define a variable, write an inequality, and solve each problem. Che...
 62.45: Define a variable, write an inequality, and solve each problem. Che...
 62.46: GEOMETRY The area of the triangle is greater than 100 square centim...
 62.47: For Exercises 4750, define a variable, write an inequality, and sol...
 62.48: For Exercises 4750, define a variable, write an inequality, and sol...
 62.49: For Exercises 4750, define a variable, write an inequality, and sol...
 62.50: For Exercises 4750, define a variable, write an inequality, and sol...
 62.51: REASONING Explain why you can use either the Multiplication Propert...
 62.52: OPEN ENDED Describe a reallife situation that can be represented b...
 62.53: CHALLENGE Give a counterexample to show that each statement is not ...
 62.54: FIND THE ERROR Ilonia and Zachary are solving 9b 18. Who is correc...
 62.55: Writing in Math Use the information about the cases of beverages on...
 62.56: Juans longdistance phone company charges 9 for each minute. Which ...
 62.57: REVIEW The table shows the results of a number cube being rolled. W...
 62.58: Solve each inequality. Check your solution, and graph it on a numbe...
 62.59: Solve each inequality. Check your solution, and graph it on a numbe...
 62.60: Solve each inequality. Check your solution, and graph it on a numbe...
 62.61: GYMS To join a gym, Cristina paid an initial fee of $120, plus $10 ...
 62.62: Write an equation in standard form for a line that passes through e...
 62.63: Write an equation in standard form for a line that passes through e...
 62.64: Write an equation in standard form for a line that passes through e...
 62.65: PREREQUISITE SKILL Solve each equation. 5x  3 = 32
 62.66: PREREQUISITE SKILL Solve each equation. _14g + 5 6 = 9
 62.67: PREREQUISITE SKILL Solve each equation. 6y  1 = 4y + 23
 62.68: PREREQUISITE SKILL Solve each equation. 2(p  4) = 7(p + 3)
Solutions for Chapter 62: Solving Inequalities by Multiplication and Division
Full solutions for Algebra 1, Student Edition (MERRILL ALGEBRA 1)  1st Edition
ISBN: 9780078738227
Solutions for Chapter 62: Solving Inequalities by Multiplication and Division
Get Full SolutionsAlgebra 1, Student Edition (MERRILL ALGEBRA 1) was written by and is associated to the ISBN: 9780078738227. Since 68 problems in chapter 62: Solving Inequalities by Multiplication and Division have been answered, more than 35259 students have viewed full stepbystep solutions from this chapter. Chapter 62: Solving Inequalities by Multiplication and Division includes 68 full stepbystep solutions. This textbook survival guide was created for the textbook: Algebra 1, Student Edition (MERRILL ALGEBRA 1) , edition: 1. This expansive textbook survival guide covers the following chapters and their solutions.

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!

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

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

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

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.

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

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Rank r (A)
= number of pivots = dimension of column space = dimension of row 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).

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

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

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).

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

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.