 1.6.1: Solve and graph the solution set.4x  3 7 2x + 7
 1.6.2: Solve and graph the solution set.8x + 1 5x  5
 1.6.3: Solve and graph the solution set.x + 6 6 5x  6
 1.6.4: Solve and graph the solution set.3  x 6 4x + 7
 1.6.5: Solve and graph the solution set.4  2x 2x + 16
 1.6.6: Solve and graph the solution set.3x  1 7 6x + 5
 1.6.7: Solve and graph the solution set. 14  5y 8y  8
 1.6.8: Solve and graph the solution set.8x  7 6 6x + 3
 1.6.9: Solve and graph the solution set.7x  7 7 5x + 5
 1.6.10: Solve and graph the solution set.12  8y 10y  6
 1.6.11: Solve and graph the solution set.3x  3 + 2x 1  7x  9
 1.6.12: Solve and graph the solution set.5y  5 + y 2  6y  8
 1.6.13: Solve and graph the solution set. 34 x  58 + 23 x
 1.6.14: Solve and graph the solution set. 56 x 34 + 83 x
 1.6.15: Solve and graph the solution set.4x1x  22 6 212x  121x  32
 1.6.16: Solve and graph the solution set.1x + 121x + 22 7 x1x + 12
 1.6.17: Find the domain of the function.h1x2 = 2x  7
 1.6.18: Find the domain of the function.g1x2 = 2x + 8
 1.6.19: Find the domain of the function.f 1x2 = 21  5x + 2
 1.6.20: Find the domain of the function.f 1x2 = 22x + 3  4
 1.6.21: Find the domain of the function.g1x2 = 524 + x
 1.6.22: Find the domain of the function.h1x2 = x28  x
 1.6.23: Solve and write interval notation for the solution set. Then graph ...
 1.6.24: Solve and write interval notation for the solution set. Then graph ...
 1.6.25: Solve and write interval notation for the solution set. Then graph ...
 1.6.26: Solve and write interval notation for the solution set. Then graph ...
 1.6.27: Solve and write interval notation for the solution set. Then graph ...
 1.6.28: Solve and write interval notation for the solution set. Then graph ...
 1.6.29: Solve and write interval notation for the solution set. Then graph ...
 1.6.30: Solve and write interval notation for the solution set. Then graph ...
 1.6.31: Solve and write interval notation for the solution set. Then graph ...
 1.6.32: Solve and write interval notation for the solution set. Then graph ...
 1.6.33: Solve and write interval notation for the solution set. Then graph ...
 1.6.34: Solve and write interval notation for the solution set. Then graph ...
 1.6.35: Solve and write interval notation for the solution set. Then graph ...
 1.6.36: Solve and write interval notation for the solution set. Then graph ...
 1.6.37: Solve and write interval notation for the solution set. Then graph ...
 1.6.38: Solve and write interval notation for the solution set. Then graph ...
 1.6.39: Solve and write interval notation for the solution set. Then graph ...
 1.6.40: Solve and write interval notation for the solution set. Then graph ...
 1.6.41: Solve and write interval notation for the solution set. Then graph ...
 1.6.42: Solve and write interval notation for the solution set. Then graph ...
 1.6.43: Information Technology. The equation y = 31.7x + 487 estimates the ...
 1.6.44: Televisions per Household. The equation y = 1.393x + 19.593 estimat...
 1.6.45: Moving Costs. Acme Movers charges $100 plus $30 per hour to move a ...
 1.6.46: Investment Income. Gina plans to invest $12,000, part at 4% simple ...
 1.6.47: Investment Income. Dillon plans to invest $7500, part at 4% simple ...
 1.6.48: Investment Income. A university invests $600,000 at simple interest...
 1.6.49: Investment Income. A foundation invests $50,000 at simple interest,...
 1.6.50: Income Plans. Tori can be paid in one of two ways for selling insur...
 1.6.51: Income Plans. Achal can be paid in one of two ways for the furnitur...
 1.6.52: Income Plans. Jeanette can be paid in one of two ways for painting ...
 1.6.53: In each of Exercises 5356, fill in the blank(s) with the correct te...
 1.6.54: In each of Exercises 5356, fill in the blank(s) with the correct te...
 1.6.55: In each of Exercises 5356, fill in the blank(s) with the correct te...
 1.6.56: In each of Exercises 5356, fill in the blank(s) with the correct te...
 1.6.57: Solve. 2x 5  7x 6 7 + x
 1.6.58: Solve.x 3x  2 2  x
 1.6.59: Solve.3y 6 4  5y 6 5 + 3y
 1.6.60: Solve.y  10 6 5y + 6 y + 10
Solutions for Chapter 1.6: Solving Linear Inequalities
Full solutions for College Algebra: Graphs and Models  5th Edition
ISBN: 9780321783950
Solutions for Chapter 1.6: Solving Linear Inequalities
Get Full SolutionsSince 60 problems in chapter 1.6: Solving Linear Inequalities have been answered, more than 26102 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: College Algebra: Graphs and Models, edition: 5. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 1.6: Solving Linear Inequalities includes 60 full stepbystep solutions. College Algebra: Graphs and Models was written by and is associated to the ISBN: 9780321783950.

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

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.

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

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.

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.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

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.

Iterative method.
A sequence of steps intended to approach the desired solution.

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 inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

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.

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

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!

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

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