Chapter 1

Determine whether each statement is true or false. If it is false, tell why. Every real number is a complex number.

Concept Check Exercises \(1-8\) should be done mentally. They will prepare you for some of the applications found in this exercise set. If a train travels at 80 mph for 15 min, what is the distance traveled?

Decide whether each statement is true or false. The solution set of \(2 x+5=x-3\) is \(\\{-8\\}\)

Match the equation in Column I with its solution \((s)\) in Column II. A. \(\pm 5 i\) B. \(\pm 2 \sqrt{5}\) C. \(\pm i \sqrt{5}\) D. \(5\) E. \(\pm \sqrt{5} \quad\) F. \(-5\) G. \(\pm 5\) H. \(\pm 2 i \sqrt{5}\) $$x^{2}=25$$

Determine whether each statement is true or false. If it is false, tell why. No real number is a pure imaginary number.

Decide what values of the variable cannot possibly be solutions for each equation. Do not solve. $$\frac{2}{x+1}+\frac{3}{5 x-2}=0$$

Concept Check Exercises \(1-8\) should be done mentally. They will prepare you for some of the applications found in this exercise set. If \(120 \mathrm{L}\) of an acid solution is \(75 \%\) acid, how much pure acid is there in the mixture?

Concept Check Match the inequality in each exercise in Column I with its equivalent interval notation in Column II. A. \((-2,6]\) B. \([-2,6)\) C. \((-\infty,-6]\) D. \([6, \infty)\) E. \((-\infty,-3) \cup(3, \infty)\) F. \((-\infty,-6)\) G. \((0,8)\) H. \((-\infty, \infty)\) I. \([-6, \infty)\) J. \(\quad(-\infty, 6]\) $$x \leq 6$$

Decide whether each statement is true or false. The equation \(5(x-8)=5 x-40\) is an example of an identity.

Match the equation in Column I with its solution \((s)\) in Column II. A. \(\pm 5 i\) B. \(\pm 2 \sqrt{5}\) C. \(\pm i \sqrt{5}\) D. \(5\) E. \(\pm \sqrt{5} \quad\) F. \(-5\) G. \(\pm 5\) H. \(\pm 2 i \sqrt{5}\) $$x^{2}=-25$$

Determine whether each statement is true or false. If it is false, tell why. Every pure imaginary number is a complex number.

Decide what values of the variable cannot possibly be solutions for each equation. Do not solve. $$\frac{3}{x-2}+\frac{1}{x+1}=\frac{3}{x^{2}-x-2}$$

Concept Check Exercises \(1-8\) should be done mentally. They will prepare you for some of the applications found in this exercise set. If a person invests \(\$ 500\) at \(2 \%\) simple interest for 4 yr, how much interest is earned?

Match the equation in Column I with its solution \((s)\) in Column II. A. \(\pm 5 i\) B. \(\pm 2 \sqrt{5}\) C. \(\pm i \sqrt{5}\) D. \(5\) E. \(\pm \sqrt{5} \quad\) F. \(-5\) G. \(\pm 5\) H. \(\pm 2 i \sqrt{5}\) $$x^{2}+5=0$$

Determine whether each statement is true or false. If it is false, tell why. A number can be both real and complex.

Decide what values of the variable cannot possibly be solutions for each equation. Do not solve. $$\frac{2}{x+3}-\frac{5}{x-1}=\frac{-5}{x^{2}+2 x-3}$$

Decide whether each statement is true or false. It is possible for a linear equation to have exactly two solutions.

Match the equation in Column I with its solution \((s)\) in Column II. A. \(\pm 5 i\) B. \(\pm 2 \sqrt{5}\) C. \(\pm i \sqrt{5}\) D. \(5\) E. \(\pm \sqrt{5} \quad\) F. \(-5\) G. \(\pm 5\) H. \(\pm 2 i \sqrt{5}\) $$x^{2}-5=0$$

Use the following facts. If \(x\) represents an integer, then \(x+1\) represents the next consecutive integer. If \(x\) represents an even integer, then \(x+2\) represents the next consecutive even integer. If \(x\) represents an odd integer, then \(x+2\) represents the next consecutive odd integer. Find two consecutive integers whose product is 56

Decide what values of the variable cannot possibly be solutions for each equation. Do not solve. $$\frac{1}{4 x}-\frac{2}{x}=3$$

Match the equation in Column I with its solution \((s)\) in Column II. A. \(\pm 5 i\) B. \(\pm 2 \sqrt{5}\) C. \(\pm i \sqrt{5}\) D. \(5\) E. \(\pm \sqrt{5} \quad\) F. \(-5\) G. \(\pm 5\) H. \(\pm 2 i \sqrt{5}\) $$x^{2}=-20$$

Determine whether each statement is true or false. If it is false, tell why. A complex number might not be a pure imaginary number.

Use the following facts. If \(x\) represents an integer, then \(x+1\) represents the next consecutive integer. If \(x\) represents an even integer, then \(x+2\) represents the next consecutive even integer. If \(x\) represents an odd integer, then \(x+2\) represents the next consecutive odd integer. Find two consecutive integers whose product is \(110 .\)

Decide what values of the variable cannot possibly be solutions for each equation. Do not solve. $$\frac{5}{2 x}+\frac{2}{x}=6$$

Sale Price Suppose that a computer that originally sold for \(x\) dollars has been discounted \(60 \%\). Which one of the following expressions does not represent its sale price? A. \(x-0.60 x\) B. \(0.40 x\) C. \(\frac{4}{10} x\) D. \(x-0.60\)

Match the equation in Column I with its solution \((s)\) in Column II. A. \(\pm 5 i\) B. \(\pm 2 \sqrt{5}\) C. \(\pm i \sqrt{5}\) D. \(5\) E. \(\pm \sqrt{5} \quad\) F. \(-5\) G. \(\pm 5\) H. \(\pm 2 i \sqrt{5}\) $$x^{2}=20$$

Identify each number as real, complex, pure imaginary, or nonreal complex. (More than one of these descriptions will apply. ) $$-4$$

Use the following facts. If \(x\) represents an integer, then \(x+1\) represents the next consecutive integer. If \(x\) represents an even integer, then \(x+2\) represents the next consecutive even integer. If \(x\) represents an odd integer, then \(x+2\) represents the next consecutive odd integer. Find two consecutive even integers whose product is 168 .

Consider the following problem. One number is 3 less than 6 times a second number. Their sum is \(46 .\) Find the numbers. If \(x\) represents the second number, which equation is correct for solving this problem? A. \(46-(x+3)=6 x\) B. \((3-6 x)+x=46\) C. \(46-(3-6 x)=x\) D. \((6 x-3)+x=46\)

Solve each equation. $$\frac{2 x+5}{2}-\frac{3 x}{x-2}=x$$

Which one is not a linear equation? A. \(5 x+7(x-1)=-3 x\) B. \(9 x^{2}-4 x+3=0\) C. \(7 x+8 x=13 x\) D. \(0.04 x-0.08 x=0.40\)

Match the equation in Column I with its solution \((s)\) in Column II. A. \(\pm 5 i\) B. \(\pm 2 \sqrt{5}\) C. \(\pm i \sqrt{5}\) D. \(5\) E. \(\pm \sqrt{5} \quad\) F. \(-5\) G. \(\pm 5\) H. \(\pm 2 i \sqrt{5}\) $$x-5=0$$

Identify each number as real, complex, pure imaginary, or nonreal complex. (More than one of these descriptions will apply. ) $$0$$

Use the following facts. If \(x\) represents an integer, then \(x+1\) represents the next consecutive integer. If \(x\) represents an even integer, then \(x+2\) represents the next consecutive even integer. If \(x\) represents an odd integer, then \(x+2\) represents the next consecutive odd integer. Find two consecutive even integers whose product is 224

Unknown Numbers Consider the following problem. The difference between seven times a number and 9 is equal to five times the sum of the number and 2. Find the number. If \(x\) represents the number, which equation is correct for solving this problem? A. \(7 x-9=5(x+2)\) B. \(9-7 x=5(x+2)\) C. \(7 x-9=5 x+2\) D. \(9-7 x=5 x+2\)

Solve each equation. $$\frac{4 x+3}{4}-\frac{2 x}{x+1}=x$$

Match the equation in Column I with its solution \((s)\) in Column II. A. \(\pm 5 i\) B. \(\pm 2 \sqrt{5}\) C. \(\pm i \sqrt{5}\) D. \(5\) E. \(\pm \sqrt{5} \quad\) F. \(-5\) G. \(\pm 5\) H. \(\pm 2 i \sqrt{5}\) $$x+5=0$$

Solve each problem. Perimeter of a Rectangle The perimeter of a rectangle is \(294 \mathrm{cm}\). The width is \(57 \mathrm{cm} .\) Find the length.

Identify each number as real, complex, pure imaginary, or nonreal complex. (More than one of these descriptions will apply. ) $$13 i$$

Use the following facts. If \(x\) represents an integer, then \(x+1\) represents the next consecutive integer. If \(x\) represents an even integer, then \(x+2\) represents the next consecutive even integer. If \(x\) represents an odd integer, then \(x+2\) represents the next consecutive odd integer. Find two consecutive odd integers whose product is 63

Solve each equation. $$|3 x-1|=2$$

Solve each equation. $$\frac{x}{x-3}=\frac{3}{x-3}+3$$

Solve each equation. $$5 x+4=3 x-4$$

Use Choices \(A-D\) to answer each question. A. \(3 x^{2}-17 x-6=0\) B. \((2 x+5)^{2}=7\) C. \(x^{2}+x=12\) D. \((3 x-1)(x-7)=0\) Which equation is set up for direct use of the zero-factor property? Solve it.

Solve each problem. Perimeter of a Storage Shed Michael Gomski must build a rectangular storage shed. He wants the length to be 6 ft greater than the width, and the perimeter will be \(44 \mathrm{ft}\). Find the length and the width of the shed.

Identify each number as real, complex, pure imaginary, or nonreal complex. (More than one of these descriptions will apply. ) $$-7 i$$

Use the following facts. If \(x\) represents an integer, then \(x+1\) represents the next consecutive integer. If \(x\) represents an even integer, then \(x+2\) represents the next consecutive even integer. If \(x\) represents an odd integer, then \(x+2\) represents the next consecutive odd integer. Find two consecutive odd integers whose product is 143

Solve each equation. $$|4 x+2|=5$$

Solve each equation. $$\frac{x}{x-4}=\frac{4}{x-4}+4$$

Solve each equation. $$9 x+11=7 x+1$$