Chapter 1

Solve each absolute value equation or indicate that the equation has no solution. $$ |x+1|+6=2 $$

Combine the types of equations we have discussed in this section. Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. \(2(x+2)+2 x=4(x+1)\)

In your own words, describe a step-by-step approach for solving algebraic word problems.

Perform the indicated operations and write the result in standard form. $$ \frac{4}{(2+i)(3-i)} $$

In Exercises \(75-82,\) compute the discriminant. Then determine the number and type of solutions for the given equation. $$ x^{2}-4 x-5=0 $$

List the quadrant or quadrants satisfying each condition. $$ x y>0 $$

Solve each absolute value inequality. $$\left|\frac{2 x+2}{4}\right| \geq 2$$

Solve each absolute value equation or indicate that the equation has no solution. $$ |2 x-1|+3=3 $$

Combine the types of equations we have discussed in this section. Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. \(\frac{2}{x}+\frac{1}{2}=\frac{3}{4}\)

Write an original word problem that can be solved using a linear equation. Then solve the problem.

Perform the indicated operations and write the result in standard form. $$ \frac{1+i}{1+2 i}+\frac{1-i}{1-2 i} $$

In Exercises \(75-82,\) compute the discriminant. Then determine the number and type of solutions for the given equation. $$ 4 x^{2}-2 x+3=0 $$

List the quadrant or quadrants satisfying each condition. $$ \frac{y}{x}<0 $$

Solve each absolute value inequality. $$\left|\frac{3 x-3}{9}\right| \geq 1$$

Solve each absolute value equation or indicate that the equation has no solution. $$ |3 x-2|+4=4 $$

Combine the types of equations we have discussed in this section. Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. \(\frac{3}{x}-\frac{1}{6}=\frac{1}{3}\)

Explain what it means to solve a formula for a variable.

Perform the indicated operations and write the result in standard form. $$ \frac{8}{1+\frac{2}{i}} $$

In Exercises \(75-82,\) compute the discriminant. Then determine the number and type of solutions for the given equation. $$ 2 x^{2}-11 x+3=0 $$

List the quadrant or quadrants satisfying each condition. $$ x^{3}>0 \text { and } y^{3}<0 $$

Absolute value expressions are equal when the expressions inside the absolute value bars are equal to or opposites of each other. $$ |3 x-1|=|x+5| $$

Solve each absolute value inequality. $$\left|3-\frac{2}{3} x\right|>5$$

Combine the types of equations we have discussed in this section. Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. \(\frac{4}{x-2}+\frac{3}{x+5}=\frac{7}{(x+5)(x-2)}\)

Did you have difficulties solving some of the problems that were assigned in this Exercise Set? Discuss what you did if this happened to you. Did your course of action enhance your ability to solve algebraic word problems?

Exercises \(78-80\) will help you prepare for the material covered in the next section. Factor: \(2 x^{2}+7 x-4\)

In Exercises \(75-82,\) compute the discriminant. Then determine the number and type of solutions for the given equation. $$ 2 x^{2}+11 x-6=0 $$

List the quadrant or quadrants satisfying each condition. $$ x^{3}<0 \text { and } y^{3}>0 $$

Absolute value expressions are equal when the expressions inside the absolute value bars are equal to or opposites of each other. $$ |2 x-7|=|x+3| $$

Solve each absolute value inequality. $$\left|3-\frac{3}{4} x\right|>9$$

Combine the types of equations we have discussed in this section. Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. \(\frac{1}{x-1}=\frac{1}{(2 x+3)(x-1)}+\frac{4}{2 x+3}\)

Exercises \(78-80\) will help you prepare for the material covered in the next section. Factor: \(x^{2}-6 x+9\)

In Exercises \(75-82,\) compute the discriminant. Then determine the number and type of solutions for the given equation. $$ x^{2}-2 x+1=0 $$

Solve each absolute value inequality. $$3|x-1|+2 \geq 8$$

Combine the types of equations we have discussed in this section. Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. \(\frac{4 x}{x+3}-\frac{12}{x-3}=\frac{4 x^{2}+36}{x^{2}-9}\)

A tennis club offers two payment options. Members can pay a monthly fee of \(\$ 30\) plus \(\$ 5\) per hour for court rental time. The second option has no monthly fee, but court time costs \(\$ 7.50\) per hour. a. Write a mathematical model representing total monthly costs for each option for \(x\) hours of court rental time. b. Use a graphing utility to graph the two models in a \([0,15,1]\) by \([0,120,20]\) viewing rectangle. c. Use your utility's trace or intersection feature to determine where the two graphs intersect. Describe what the coordinates of this intersection point represent in practical terms. d. Verify part (c) using an algebraic approach by setting the two models equal to one another and determining how many hours one has to rent the court so that the two plans result in identical monthly costs.

Exercises \(78-80\) will help you prepare for the material covered in the next section. Evaluate $$ \frac{-b-\sqrt{b^{2}-4 a c}}{2 a} $$ for \(a=2, b=9,\) and \(c=-5\)

In Exercises \(75-82,\) compute the discriminant. Then determine the number and type of solutions for the given equation. $$ 3 x^{2}=2 x-1 $$

Absolute value expressions are equal when the expressions inside the absolute value bars are equal to or opposites of each other. (graph cannot copy for a,b,c,d,e,f) $$ y=\sqrt{x-4}+\sqrt{x+4}-4 $$

Solve each absolute value inequality. $$5|2 x+1|-3 \geq 9$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. By modeling attitudes of college freshmen from 1969 through \(2009,\) I can make precise predictions about the attitudes of the freshman class of 2020.

In Exercises \(75-82,\) compute the discriminant. Then determine the number and type of solutions for the given equation. $$ x^{2}-3 x-7=0 $$

Absolute value expressions are equal when the expressions inside the absolute value bars are equal to or opposites of each other. (graph cannot copy for a,b,c,d,e,f) $$y=x^{\frac{1}{3}}+2 x^{\frac{1}{6}}-3$$

Solve each absolute value inequality. $$-2|x-4| \geq-4$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I find the hardest part in solving a word problem is writing the equation that models the verbal conditions.

In Exercises \(75-82,\) compute the discriminant. Then determine the number and type of solutions for the given equation. $$ 3 x^{2}+4 x-2=0 $$

Solve each absolute value inequality. $$-3|x+7| \geq-27$$

Solve each equation in Exercises \(83-108\) by the method of your choice. $$ 2 x^{2}-x=1 $$

Absolute value expressions are equal when the expressions inside the absolute value bars are equal to or opposites of each other. (graph cannot copy for a,b,c,d,e,f) $$y=(x+2)^{2}-9(x+2)+20$$

Solve each absolute value inequality. $$-4|1-x|<-16$$

Solve each equation in Exercises \(83-108\) by the method of your choice. $$ 3 x^{2}-4 x=4 $$