91Ó°ÊÓ

Solve each rational inequality in Exercises \(29-48,\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ \frac{x}{x+2} \geq 2 $$

Solve each equation in by making an appropriate substitution. $$ 2 x-7 \sqrt{x}-30=0 $$

Solve each equation in Exercises \(39-54\) by completing the square. $$ x^{2}-2 x-5=0 $$

Solve each equation in Exercises \(39-54\) by completing the square. $$ x^{2}+4 x+1=0 $$

Exercises \(31-50\) contain equations with variables in denominators. For each equation, a. Write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. $$ \frac{3}{x+2}+\frac{2}{x-2}=\frac{8}{(x+2)(x-2)} $$

Solve each linear inequality in Exercises 27-48 and graph the solution set on a number line. Express the solution set using interval notation. $$\frac{x-4}{6} \geq \frac{x-2}{9}+\frac{5}{18}$$

Solve each equation in by making an appropriate substitution. $$ x^{-2}-x^{-1}-20=0 $$

Solve each rational inequality in Exercises \(29-48,\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ \frac{3}{x+3}>\frac{3}{x-2} $$

Solve each equation in Exercises \(39-54\) by completing the square. $$ x^{2}+6 x-5=0 $$

Explain how to add complex numbers. Provide an example with your explanation.