 3.7.3.7.1: Graph each inequality. See Examples 1 and 2.x 6 2
 3.7.3.7.2: Graph each inequality. See Examples 1 and 2.x 7 3
 3.7.3.7.3: Graph each inequality. See Examples 1 and 2.x  y 7
 3.7.3.7.4: Graph each inequality. See Examples 1 and 2.3x + y 1
 3.7.3.7.5: Graph each inequality. See Examples 1 and 2.3x + y 7 6
 3.7.3.7.6: Graph each inequality. See Examples 1 and 2.2x + y 7 2
 3.7.3.7.7: Graph each inequality. See Examples 1 and 2.y 2x
 3.7.3.7.8: Graph each inequality. See Examples 1 and 2.y 3x
 3.7.3.7.9: Graph each inequality. See Examples 1 and 2.2x + 4y 8
 3.7.3.7.10: Graph each inequality. See Examples 1 and 2.2x + 6y 12
 3.7.3.7.11: Graph each inequality. See Examples 1 and 2.5x + 3y 7 15
 3.7.3.7.12: Graph each inequality. See Examples 1 and 2.2x + 5y 6 20
 3.7.3.7.13: Graph each union or intersection. See Examples 3 and 4.x 3 and y 2
 3.7.3.7.14: Graph each union or intersection. See Examples 3 and 4.x 3 or y 2
 3.7.3.7.15: Graph each union or intersection. See Examples 3 and 4.x 2 or y 4
 3.7.3.7.16: Graph each union or intersection. See Examples 3 and 4.x 2 and y 4
 3.7.3.7.17: Graph each union or intersection. See Examples 3 and 4.x  y 6 3 an...
 3.7.3.7.18: Graph each union or intersection. See Examples 3 and 4.2x 7 y and y...
 3.7.3.7.19: Graph each union or intersection. See Examples 3 and 4.x + y 3 or x...
 3.7.3.7.20: Graph each union or intersection. See Examples 3 and 4.x  y 3 or x...
 3.7.3.7.21: Graph each inequality.y 2
 3.7.3.7.22: Graph each inequality.y 4
 3.7.3.7.23: Graph each inequality.x  6y 6 12
 3.7.3.7.24: Graph each inequality.x  4y 6 8
 3.7.3.7.25: Graph each inequality.x 7 5
 3.7.3.7.26: Graph each inequality.y 2
 3.7.3.7.27: Graph each inequality.2x + y 4
 3.7.3.7.28: Graph each inequality.3x + y 9
 3.7.3.7.29: Graph each inequality.x  3y 6 0
 3.7.3.7.30: Graph each inequality.x + 2y 7 0
 3.7.3.7.31: Graph each inequality.3x  2y 12
 3.7.3.7.32: Graph each inequality.2x  3y 9
 3.7.3.7.33: Graph each inequality.x  y 7 2 or y 6 5
 3.7.3.7.34: Graph each inequality.x  y 6 3 or x 7 4
 3.7.3.7.35: Graph each inequality.x + y 1 and y 1
 3.7.3.7.36: Graph each inequality.y x and 2x  4y 6
 3.7.3.7.37: Graph each inequality.2x + y 7 4 or x 1
 3.7.3.7.38: Graph each inequality.3x + y 6 9 or y 2
 3.7.3.7.39: Graph each inequality.x 2 and x 1
 3.7.3.7.40: Graph each inequality.x 4 and x 3
 3.7.3.7.41: Graph each inequality.x + y 0 or 3x  6y 12
 3.7.3.7.42: Graph each inequality.x + y 0 and 3x  6y 12
 3.7.3.7.43: Graph each inequality.2x  y 7 3 and x 7 0
 3.7.3.7.44: Graph each inequality.2x  y 7 3 or x 7 0
 3.7.3.7.45: Match each inequality with its graph.y 2x + 3
 3.7.3.7.46: Match each inequality with its graph.y 6 2x + 3
 3.7.3.7.47: Match each inequality with its graph.y 7 2x + 3
 3.7.3.7.48: Match each inequality with its graph.y 2x + 3
 3.7.3.7.49: Write the inequality whose graph is given.3355 3 4 1 321 2 4 5 xy2
 3.7.3.7.50: Write the inequality whose graph is given.1413355 3 4 1 321 2 4 5 x...
 3.7.3.7.51: Write the inequality whose graph is given.13355 3 4 1 321 2 4 5 xy 52.
 3.7.3.7.52: Write the inequality whose graph is given.1413355 3 4 1 321 2 4 5 x...
 3.7.3.7.53: Write the inequality whose graph is given.251413355 3 4 1 321 2 4 5...
 3.7.3.7.54: Write the inequality whose graph is given.251413355 3 4 1 321 2 4 5...
 3.7.3.7.55: Write the inequality whose graph is given.55 3 4 1 3
 3.7.3.7.56: Write the inequality whose graph is given.251413355
 3.7.3.7.57: Evaluate each expression. See Sections 1.3 and 1.4.23
 3.7.3.7.58: Evaluate each expression. See Sections 1.3 and 1.4.32
 3.7.3.7.59: Evaluate each expression. See Sections 1.3 and 1.4.52
 3.7.3.7.60: Evaluate each expression. See Sections 1.3 and 1.4.1 522
 3.7.3.7.61: Evaluate each expression. See Sections 1.3 and 1.4.1 224
 3.7.3.7.62: Evaluate each expression. See Sections 1.3 and 1.4.24
 3.7.3.7.63: Evaluate each expression. See Sections 1.3 and 1.4.a35b3
 3.7.3.7.64: Evaluate each expression. See Sections 1.3 and 1.4.a27b2
 3.7.3.7.65: Find the domain and the range of each relation. Determine whether t...
 3.7.3.7.66: Find the domain and the range of each relation. Determine whether t...
 3.7.3.7.67: Explain when a dashed boundary line should be used in the graph of ...
 3.7.3.7.68: Explain why, after the boundary line is sketched, we test a point o...
 3.7.3.7.69: Solve.ChrisCraft manufactures boats out of Fiberglas and wood.Fibe...
 3.7.3.7.70: Rheem AboZahrah decides that she will study at most20 hours every ...
Solutions for Chapter 3.7: Graphing Linear Inequalities
Full solutions for Intermediate Algebra  6th Edition
ISBN: 9780321785046
Solutions for Chapter 3.7: Graphing Linear Inequalities
Get Full SolutionsSince 70 problems in chapter 3.7: Graphing Linear Inequalities have been answered, more than 66825 students have viewed full stepbystep solutions from this chapter. Intermediate Algebra was written by and is associated to the ISBN: 9780321785046. This textbook survival guide was created for the textbook: Intermediate Algebra, edition: 6. Chapter 3.7: Graphing Linear Inequalities includes 70 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

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

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 IIĀ· Condition numbers measure the sensitivity of the output to change in the input.

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

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

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!).

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

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.

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

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.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

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).