 2.1.1: . A(n) _______ is a statement that two algebraic expressions are eq...
 2.1.2: A linear equation in one variable is an equation that can be writte...
 2.1.3: When solving an equation, it is possible to introduce a(n) _______ ...
 2.1.4: Many reallife problems can be solved using readymade equations ca...
 2.1.5: Is the equation x + 1 = 3 an identity, a conditional equation, or a...
 2.1.6: How can you clear the equation x 2 + 1 = 1 4 of fractions?
 2.1.7: In Exercises 710, determine whether each value of x is a solution o...
 2.1.8: In Exercises 710, determine whether each value of x is a solution o...
 2.1.9: In Exercises 710, determine whether each value of x is a solution o...
 2.1.10: In Exercises 710, determine whether each value of x is a solution o...
 2.1.11: In Exercises 1118, determine whether the equation is an identity, a...
 2.1.12: In Exercises 1118, determine whether the equation is an identity, a...
 2.1.13: In Exercises 1118, determine whether the equation is an identity, a...
 2.1.14: In Exercises 1118, determine whether the equation is an identity, a...
 2.1.15: In Exercises 1118, determine whether the equation is an identity, a...
 2.1.16: In Exercises 1118, determine whether the equation is an identity, a...
 2.1.17: In Exercises 1118, determine whether the equation is an identity, a...
 2.1.18: In Exercises 1118, determine whether the equation is an identity, a...
 2.1.19: In Exercises 1922, solve the equation using two methods. Then expla...
 2.1.20: In Exercises 1922, solve the equation using two methods. Then expla...
 2.1.21: In Exercises 1922, solve the equation using two methods. Then expla...
 2.1.22: In Exercises 1922, solve the equation using two methods. Then expla...
 2.1.23: In Exercises 23 42, solve the equation (if possible). 23. 3x 5 = 2x...
 2.1.24: In Exercises 23 42, solve the equation (if possible). 24. 5x + 3 = ...
 2.1.25: In Exercises 23 42, solve the equation (if possible). 25. 3(y 5) = ...
 2.1.26: In Exercises 23 42, solve the equation (if possible). 26. 4(z 3) + ...
 2.1.27: In Exercises 23 42, solve the equation (if possible). 27. x 5 x 2 =...
 2.1.28: In Exercises 23 42, solve the equation (if possible). 28. 3x 4 + x ...
 2.1.29: In Exercises 23 42, solve the equation (if possible). 29. 5x 4 5x +...
 2.1.30: In Exercises 23 42, solve the equation (if possible). 30. 10x + 3 5...
 2.1.31: In Exercises 23 42, solve the equation (if possible).31. 2 5 (z 4) ...
 2.1.32: In Exercises 23 42, solve the equation (if possible). 32. 3x 2 + 1 ...
 2.1.33: In Exercises 23 42, solve the equation (if possible). 33. 17 + y y ...
 2.1.34: In Exercises 23 42, solve the equation (if possible).34. x 11 x = x...
 2.1.35: In Exercises 23 42, solve the equation (if possible). 35. 1 x 3 + 1...
 2.1.36: In Exercises 23 42, solve the equation (if possible).36. 1 x 2 + 3 ...
 2.1.37: In Exercises 23 42, solve the equation (if possible). 37. 1 x + 2 x...
 2.1.38: In Exercises 23 42, solve the equation (if possible). 38. 3 = 2 + 2...
 2.1.39: In Exercises 23 42, solve the equation (if possible). 39. 2 (x 4)(x...
 2.1.40: In Exercises 23 42, solve the equation (if possible). 40. 2 x(x 2) ...
 2.1.41: In Exercises 23 42, solve the equation (if possible). 41. 3 x2 3x +...
 2.1.42: In Exercises 23 42, solve the equation (if possible). 23. 3x 5 = 2x...
 2.1.43: In Exercises 43 48, solve for the indicated variable. 43. Area of a...
 2.1.44: In Exercises 43 48, solve for the indicated variable. 43. Area of a...
 2.1.45: In Exercises 43 48, solve for the indicated variable. 43. Area of a...
 2.1.46: In Exercises 43 48, solve for the indicated variable. 43. Area of a...
 2.1.47: In Exercises 43 48, solve for the indicated variable. 43. Area of a...
 2.1.48: In Exercises 43 48, solve for the indicated variable. 43. Area of a...
 2.1.49: In Exercises 49 and 50, use the following information. The relation...
 2.1.50: In Exercises 49 and 50, use the following information. The relation...
 2.1.51: A room is 1.5 times as long as it is wide, and its perimeter is 25 ...
 2.1.52: A picture frame has a total perimeter of 3 meters. The height of th...
 2.1.53: To get an A in a course, you must have an average of at least 90 on...
 2.1.54: A store generates Monday through Thursday sales of $150, $125, $75,...
 2.1.55: A salesperson is driving from the office to a client, a distance of...
 2.1.56: On the first part of a 336mile trip, a salesperson averaged 58 mil...
 2.1.57: A truck driver traveled at an average speed of 55 miles per hour on...
 2.1.58: You are driving on a Canadian freeway to a town that is 300 kilomet...
 2.1.59: To determine the height of a pine tree, you measure the shadow cast...
 2.1.60: A person who is 6 feet tall walks away from a flagpole toward the t...
 2.1.61: A certificate of deposit with an initial deposit of $8000 accumulat...
 2.1.62: You plan to invest $12,000 in two funds paying 41 2% and 5% simple ...
 2.1.63: A grocer mixes peanuts that cost $2.50 per pound and walnuts that c...
 2.1.64: A forester mixes gasoline and oil to make 2 gallons of mixture for ...
 2.1.65: A store has $40,000 of inventory in notebook computers and tablet c...
 2.1.66: A store has $4500 of inventory in 8 10 picture frames and 5 7 pictu...
 2.1.67: A triangular sail has an area of 182.25 square feet. The sail has a...
 2.1.68: The figure shows three squares. The perimeter of square I is 20 inc...
 2.1.69: The volume of a rectangular package is 2304 cubic inches. The lengt...
 2.1.70: The volume of a globe is about 6255 cubic centimeters. Use a graphi...
 2.1.71: The line graph shows the temperatures (in degrees Fahrenheit) on a ...
 2.1.72: The average July 2013 temperature in the contiguous United States w...
 2.1.73: An executive flew in the corporate jet to a meeting in a city 1500 ...
 2.1.74: A gondola tower in an amusement park casts a shadow that is 80 feet...
 2.1.75: In Exercises 75 and 76, you have a uniform beam of length L with a ...
 2.1.76: In Exercises 75 and 76, you have a uniform beam of length L with a ...
 2.1.77: In Exercises 77 and 78, determine whether the statement is true or ...
 2.1.78: In Exercises 77 and 78, determine whether the statement is true or ...
 2.1.79: In Exercises 7982, write a linear equation that has the given solut...
 2.1.80: In Exercises 7982, write a linear equation that has the given solut...
 2.1.81: In Exercises 7982, write a linear equation that has the given solut...
 2.1.82: In Exercises 7982, write a linear equation that has the given solut...
 2.1.83: Describe the error in solving the equation. 1 x + 1 + 1 x 1 = 2 (x ...
 2.1.84: To determine the height of a building, you measure the shadows cast...
 2.1.85: Consider the equation 6 (x 3)(x 1) = 3 x 3 + 4 x 1 . Without perfor...
 2.1.86: Find c such that x = 2 is a solution of the linear equation 5x + 2c...
 2.1.87: In Exercises 8792, sketch the graph of the equation by hand. Verify...
 2.1.88: In Exercises 8792, sketch the graph of the equation by hand. Verify...
 2.1.89: In Exercises 8792, sketch the graph of the equation by hand. Verify...
 2.1.90: In Exercises 8792, sketch the graph of the equation by hand. Verify...
 2.1.91: In Exercises 8792, sketch the graph of the equation by hand. Verify...
 2.1.92: In Exercises 8792, sketch the graph of the equation by hand. Verify...
Solutions for Chapter 2.1: Solving Equations and Inequalities
Full solutions for Algebra and Trigonometry: Real Mathematics, Real People  7th Edition
ISBN: 9781305071735
Solutions for Chapter 2.1: Solving Equations and Inequalities
Get Full SolutionsSince 92 problems in chapter 2.1: Solving Equations and Inequalities have been answered, more than 65111 students have viewed full stepbystep solutions from this chapter. Chapter 2.1: Solving Equations and Inequalities includes 92 full stepbystep solutions. This textbook survival guide was created for the textbook: Algebra and Trigonometry: Real Mathematics, Real People, edition: 7. Algebra and Trigonometry: Real Mathematics, Real People was written by and is associated to the ISBN: 9781305071735. This expansive textbook survival guide covers the following chapters and their solutions.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

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

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.

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.

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

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

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.

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

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).

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

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

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

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

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

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

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.