Chapter 1

The given equation is either linear or equivalent to a linear equation. Solve the equation. \(\frac{2 x-1}{x+2}=\frac{4}{5}\)

A Riddle A father is four times as old as his daughter. In 6 years, he will be three times as old as she is. How old is the daughter now?

Evaluate the expression and write the result in the form a bi. $$ i^{3} $$

\(23-48\) Solve the inequality. Express the answer using interval notation. $$ |x+5| \geq 2 $$

Solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ -2<8-2 x \leq-1 $$

Find all real solutions of the equation. $$ x^{2}-7 x+10=0 $$

\(5-60\) Find all real solutions of the equation. $$ \sqrt{5-x}+1=x-2 $$

The given equation is either linear or equivalent to a linear equation. Solve the equation. \(\frac{2}{t+6}=\frac{3}{t-1}\)

A Riddle A movie star, unwilling to give his age, posed the following riddle to a gossip columnist: "Seven years ago, I was eleven times as old as my daughter. Now I am four times as old as she is." How old is the movie star?

Evaluate the expression and write the result in the form a bi. $$ (2 i)^{4} $$

\(23-48\) Solve the inequality. Express the answer using interval notation. $$ |x+1| \geq 3 $$

Solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ -3 \leq 3 x+7 \leq \frac{1}{2} $$

Find all real solutions of the equation. $$ x^{2}+30 x+200=0 $$

\(5-60\) Find all real solutions of the equation. $$ 2 x+\sqrt{x+1}=8 $$

The given equation is either linear or equivalent to a linear equation. Solve the equation. \(\frac{1}{t-1}+\frac{t}{3 t-2}=\frac{1}{3}\)

Career Home Runs During his major league career, Hank Aaron hit 41 more home runs than Babe Ruth hit during his career. Together they hit 1469 home runs. How many home runs did Babe Ruth hit?

Evaluate the expression and write the result in the form a bi. $$ i^{100} $$

\(23-48\) Solve the inequality. Express the answer using interval notation. $$ |2 x-3| \leq 0.4 $$

Solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ \frac{2}{3} \geq \frac{2 x-3}{12}>\frac{1}{6} $$

Find all real solutions of the equation. $$ 2 x^{2}+x-3=0 $$

\(5-60\) Find all real solutions of the equation. $$ x-\sqrt{x+3}=\frac{x}{2} $$

The given equation is either linear or equivalent to a linear equation. Solve the equation. \(r-2[1-3(2 r+4)]=61\)

Value of Coins \(\quad\) A change purse contains an equal number of pennies, nickels, and dimes. The total value of the coins is \(\$ 1.44 .\) How many coins of each type does the purse contain?

Evaluate the expression and write the result in the form a bi. $$ i^{1002} $$

\(23-48\) Solve the inequality. Express the answer using interval notation. $$ |5 x-2|<6 $$

Solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ -\frac{1}{2} \leq \frac{4-3 x}{5} \leq \frac{1}{4} $$

Find all real solutions of the equation. $$ 3 x^{2}+7 x+4=0 $$

\(5-60\) Find all real solutions of the equation. $$ x+2 \sqrt{x-7}=10 $$

The given equation is either linear or equivalent to a linear equation. Solve the equation. \((t-4)^{2}=(t+4)^{2}+32\)

Value of Coins Mary has \(\$ 3.00\) in nickels, dimes, and quarters. If she has twice as many dimes as quarters and five more nickels than dimes, how many coins of each type does she have?

Evaluate the expression and write the result in the form a bi. $$ \frac{1}{i} $$

\(23-48\) Solve the inequality. Express the answer using interval notation. $$ \left|\frac{x-2}{3}\right|<2 $$

Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set. $$ (x+2)(x-3)<0 $$

Find all real solutions of the equation. $$ x^{2}+3 x+1=0 $$

\(5-60\) Find all real solutions of the equation. $$ (x+5)^{2}-3(x+5)-10=0 $$

The given equation is either linear or equivalent to a linear equation. Solve the equation. \(\sqrt{3} x+\sqrt{12}=\frac{x+5}{\sqrt{3}}\)

Length of a Garden A rectangular garden is 25 \(\mathrm{ft}\) wide. If its area is 1125 \(\mathrm{ft}^{2}\) , what is the length of the garden?

Evaluate the expression and write the result in the form a bi. $$ \frac{1}{1+i} $$

\(23-48\) Solve the inequality. Express the answer using interval notation. $$ \left|\frac{x+1}{2}\right| \geq 4 $$

Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set. $$ (x-5)(x+4) \geq 0 $$

Find all real solutions of the equation. $$ 2 x^{2}-8 x+4=0 $$

\(5-60\) Find all real solutions of the equation. $$ \left(\frac{x+1}{x}\right)^{2}+4\left(\frac{x+1}{x}\right)+3=0 $$

The given equation is either linear or equivalent to a linear equation. Solve the equation. \(\frac{2}{3} X-\frac{1}{4}=\frac{1}{6} X-\frac{1}{9}\)

Width of a Pasture A pasture is twice as long as it is wide. Its area is \(115,200 \mathrm{ft}^{2} .\) How wide is the pasture?

Evaluate the expression and write the result in the form a bi. $$ \frac{2-3 i}{1-2 i} $$

\(23-48\) Solve the inequality. Express the answer using interval notation. $$ |x+6|<0.001 $$

Solve the nonlinear inequality. Express the solution using interval notation and graph the solution set. $$ x(2 x+7) \geq 0 $$

Find all real solutions of the equation. $$ x^{2}+12 x-27=0 $$

\(5-60\) Find all real solutions of the equation. $$ \left(\frac{1}{x+1}\right)^{2}-2\left(\frac{1}{x+1}\right)-8=0 $$

The given equation is either linear or equivalent to a linear equation. Solve the equation. \(\frac{2}{x}-5=\frac{6}{x}+4\)