Chapter 1

In Exercises 59–94, solve each absolute value inequality. $$ \left|\frac{2 x+2}{4}\right| \geq 2 $$

Will help you prepare for the material covered in the next section. Multiply: \((7-3 x)(-2-5 x)\)

Compute the discriminant. Then determine the number and type of solutions for the given equation. $$ x^{2}-4 x-5=0 $$

In Exercises 61–78, solve each absolute value equation or indicate that the equation has no solution. $$|2 x-1|+3=3$$

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

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

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

In Exercises 59–94, solve each absolute value inequality. $$ \left|\frac{3 x-3}{9}\right| \geq 1 $$

Will help you prepare for the material covered in the next section. Simplify: \(\sqrt{18}-\sqrt{8}\)

Compute the discriminant. Then determine the number and type of solutions for the given equation. $$ 4 x^{2}-2 x+3=0 $$

In Exercises 61–78, solve each absolute value equation or indicate that the equation has no solution. $$|3 x-2|+4=4$$

In Exercises \(75-78,\) list the quadrant or quadrants satisfying each condition. $$ \frac{y}{x}<0 $$

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

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

In Exercises 59–94, solve each absolute value inequality. $$ 3-\frac{2}{3} x |>5 $$

Will help you prepare for the material covered in the next section. Rationalize the denominator: \(\frac{7+4 \sqrt{2}}{2-5 \sqrt{2}}\)

Compute the discriminant. Then determine the number and type of solutions for the given equation. $$ 2 x^{2}-11 x+3=0 $$

Hint for Exercises 77–78: Absolute value expressions are equal when the expressions inside the absolute value bars are equal to or opposites of each other. $$|3 x-1|=|x+5|$$

In Exercises \(75-78,\) list the quadrant or quadrants satisfying each condition. \(x^{3}>0\) and \(y^{3}<0\)

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

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

In Exercises 59–94, solve each absolute value inequality. $$ \left|3-\frac{3}{4} x\right|>9 $$

Compute the discriminant. Then determine the number and type of solutions for the given equation. $$ 2 x^{2}+11 x-6=0 $$

Hint for Exercises 77–78: Absolute value expressions are equal when the expressions inside the absolute value bars are equal to or opposites of each other. $$|2 x-7|=|x+3|$$

In Exercises \(75-78,\) list the quadrant or quadrants satisfying each condition. \(x^{3}<0\) and \(y^{3}>0\)

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

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

In Exercises 59–94, solve each absolute value inequality. $$ 3|x-1|+2 \geq 8 $$

Compute the discriminant. Then determine the number and type of solutions for the given equation. $$ x^{2}-2 x+1=0 $$

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

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

In Exercises 59–94, solve each absolute value inequality. $$ 5|2 x+1|-3 \geq 9 $$

Compute the discriminant. Then determine the number and type of solutions for the given equation. $$ 3 x^{2}=2 x-1 $$

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 \(c=-5\)

Combine the types of equations we have discussed in this section. Solve equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. $$\frac{4}{x^{2}+3 x-10}-\frac{1}{x^{2}+x-6}=\frac{3}{x^{2}-x-12}$$

In Exercises 59–94, solve each absolute value inequality. $$ -2|x-4| \geq-4 $$

Compute the discriminant. Then determine the number and type of solutions for the given equation. $$ x^{2}-3 x-7=0 $$

In Exercises 59–94, solve each absolute value inequality. $$ -3|x+7| \geq-27 $$

Compute the discriminant. Then determine the number and type of solutions for the given equation. $$ 3 x^{2}+4 x-2=0 $$

In Exercises 59–94, solve each absolute value inequality. $$ -4|1-x|<-16 $$

Solve equation by the method of your choice. $$ 2 x^{2}-x=1 $$

In Exercises 59–94, solve each absolute value inequality. $$ -2|5-x|<-6 $$

Solve equation by the method of your choice. $$ 3 x^{2}-4 x=4 $$

In Exercises 59–94, solve each absolute value inequality. $$ 3 \leq|2 x-1| $$

Solve equation by the method of your choice. $$ 5 x^{2}+2=11 x $$

Find all values of \(x\) satisfying the given conditions. $$y=|5-4 x| \text { and } y=11$$

Evaluate \(x^{2}-x\) for the value of \(x\) satisfying $$4(x-2)+2=4 x-2(2-x)$$

In Exercises 59–94, solve each absolute value inequality. $$ 9 \leq|4 x+7| $$

Solve equation by the method of your choice. $$ 5 x^{2}=6-13 x $$

Find all values of \(x\) satisfying the given conditions. $$y=|2-3 x| \text { and } y=13$$