 2.1: Solve each equation, and check your solution.x + 2 = 3
 2.2: Solve each equation, and check your solution.2m + 8 = 16
 2.3: Solve each equation, and check your solution.12.5x = 63.75
 2.4: Solve each equation, and check your solution.x = 12
 2.5: Solve each equation, and check your solution.45x = 20
 2.6: Solve each equation, and check your solution.7m  5m = 12
 2.7: Solve each equation, and check your solution.5x  9 = 31x  32
 2.8: Solve each equation, and check your solution.x  2 = 8
 2.9: Solve each equation, and check your solution.x = 6
 2.10: Solve each equation, and check your solution.23x + 8 = 14x
 2.11: Solve each equation, and check your solution.4x + 213  2x2 = 6
 2.12: Solve each equation, and check your solution.6z = 14
 2.13: Solve each equation, and check your solution.31m  42 + 215 + 2m2 ...
 2.14: Solve each equation, and check your solution.0.3x + 2.11x  42 = 6.6
 2.15: Solve each equation, and check your solution.0.08x + 0.061x + 92 = ...
 2.16: Solve each equation, and check your solution.x  16.2 = 7.5
 2.17: Solve each equation, and check your solution.7m  12m  92 = 39
 2.18: Solve each equation, and check your solution.71p  22 + p = 21p + 22
 2.19: Solve each equation, and check your solution.2t + 5t  9 = 31t  42...
 2.20: Solve each equation, and check your solution.31m + 52  1 + 2m = 51...
 2.21: Solve each equation, and check your solution.0.21502 + 0.8r = 0.415...
 2.22: Solve each equation, and check your solution.2.3x + 13.7 = 1.3x + 2.9
 2.23: Solve each equation, and check your solution.213 + 7x2  11 + 15x2 = 2
 2.24: Solve each equation, and check your solution.6q  9 = 12 + 3q
 2.25: Solve each equation, and check your solution.214 + 3r2 = 31r + 12 + 11
 2.26: Solve each equation, and check your solution.r + 9 + 7r = 413 + 2r2...
 2.27: Solve each equation, and check your solution.14x  4 = 32x +34x
 2.28: Solve each equation, and check your solution.0.61100  x2 + 0.4x = ...
 2.29: Solve each equation, and check your solution.3 41z  22  1315  2z...
 2.30: Solve each equation, and check your solution.2  1m + 42 = 3m  2
 2.31: Find the measure of each marked angle.(8x 1) (3x 6)
 2.32: Find the measure of each marked angle.(3x + 10)(4x 20)
 2.33: Solve each problemThe perimeter of a certain rectangle is 16 times ...
 2.34: Solve each problemThe Ziegfield Room in Reno, Nevada, has a circula...
 2.35: Solve each problemA baseball diamond is a square with aside of 90 f...
 2.36: Give a ratio for each word phrase, writing fractions in lowest term...
 2.37: Give a ratio for each word phrase, writing fractions in lowest term...
 2.38: Give a ratio for each word phrase, writing fractions in lowest term...
 2.39: Solve each equation.p21 = 530
 2.40: Solve each equation.5 + x3 = 2  x6
 2.41: Solve each problemThe tax on a $24.00 item is $2.04. How much tax w...
 2.42: Solve each problemThe distance between two cities on a road map is ...
 2.43: Solve each problemIn the 2008 Olympics in Beijing, China, Japanese ...
 2.44: Solve each problemFind the best buy. Give the unit price to the nea...
 2.45: What is 8% of 75?
 2.46: What percent of 12 is 21?
 2.47: 36% of what number is 900?
 2.48: Solve each problem.A nurse must mix 15 L of a 10% solution of a dru...
 2.49: Solve each problem.Robert Kay invested $10,000, from which he earns...
 2.50: Solve each problem.In 1846, the vessel Yorkshire traveled from Live...
 2.51: Solve each problem.Janet Hartnett drove from Louisville to Dallas, ...
 2.52: Solve each problem.Two planes leave St. Louis at the same time. One...
 2.53: Write each inequality in interval notation, and graph it.x 4
 2.54: Write each inequality in interval notation, and graph it.x 6 7
 2.55: Write each inequality in interval notation, and graph it.5 x 6 6
 2.56: Which inequality requires reversing the inequality symbol when it i...
 2.57: Solve each inequality. Write the solution set in interval notation,...
 2.58: Solve each inequality. Write the solution set in interval notation,...
 2.59: Solve each inequality. Write the solution set in interval notation,...
 2.60: Solve each inequality. Write the solution set in interval notation,...
 2.61: Solve each inequality. Write the solution set in interval notation,...
 2.62: Solve each inequality. Write the solution set in interval notation,...
 2.63: Solve each inequality. Write the solution set in interval notation,...
 2.64: Solve each inequality. Write the solution set in interval notation,...
 2.65: Solve each problemAwilda Delgado has grades of 94 and 88 on her fir...
 2.66: Solve each problemIf nine times a number is added to 6, the result ...
 2.67: Solve.x7 = x  52
 2.68: Solve.I = prt for r
 2.69: Solve.2x 7 4
 2.70: Solve.2k  5 = 4k + 13
 2.71: Solve.0.05x + 0.02x = 4.9
 2.72: Solve.2  31x  52 = 4 + x
 2.73: Solve.9x  17x + 22 = 3x + 12  x2
 2.74: Solve.13s +12s + 7 = 56 s + 5 + 2
 2.75: Solve.A family of four with a monthly income of $3800 plans to spen...
 2.76: Solve.Athletes in vigorous training programscan eat 50 calories per...
 2.77: Solve.The Golden Gate Bridge in SanFrancisco is 2604 ft longer than...
 2.78: Solve.Find the best buy. Give the unit price to the nearest thousan...
 2.79: Solve.If 1 qt of oil must be mixed with 24 qt of gasoline, how much...
 2.80: Solve.Two trains are 390 mi apart. They start at the same time and ...
 2.81: Solve.The perimeter of a triangle is 96 m. One side istwice as long...
 2.82: Solve.The perimeter of a certain square cannot be greater than 200 ...
Solutions for Chapter 2: Linear Equations and Inequalities in One Variable
Full solutions for Beginning Algebra  11th Edition
ISBN: 9780321673480
Solutions for Chapter 2: Linear Equations and Inequalities in One Variable
Get Full SolutionsChapter 2: Linear Equations and Inequalities in One Variable includes 82 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Beginning Algebra, edition: 11. Beginning Algebra was written by and is associated to the ISBN: 9780321673480. Since 82 problems in chapter 2: Linear Equations and Inequalities in One Variable have been answered, more than 39769 students have viewed full stepbystep solutions from this chapter.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

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

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

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

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 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.

Solvable system Ax = b.
The right side b is in the column space of A.

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.

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.