Chapter 1

Solve the equation by completing the square. \(3 x^{2}-6 x-1=0\)

\(9- 46\) The given equation is either linear or equivalent to a linear equation. Solve the equation. $$ \frac{2}{3} y+\frac{1}{2}(y-3)=\frac{y+1}{4} $$

Solve the inequality. Express the answer using interval notation. $$ |x-5| \leq 3 $$

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 star?

\(9-32\) me solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ 4-3 x \leq-(1+8 x) $$

Evaluate the expression and write the result in the form \(a+b i .\) $$ (3-4 i)(5-12 i) $$

1–54 ? Find all real solutions of the equation. $$ (x+5)^{2}-3(x+5)-10=0 $$

Solve the equation by completing the square. \(4 x^{2}-x=0\)

\(9- 46\) The given equation is either linear or equivalent to a linear equation. Solve the equation. $$ \frac{1}{x}=\frac{4}{3 x}+1 $$

Solve the inequality. Express the answer using interval notation. $$ |x-9|>9 $$

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?

\(9-32\) me solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ 2(7 x-3) \leq 12 x+16 $$

Evaluate the expression and write the result in the form \(a+b i .\) $$ \left(\frac{2}{3}+12 i\right)\left(\frac{1}{6}+24 i\right) $$

1–54 ? Find all real solutions of the equation. $$ \left(\frac{x+1}{x}\right)^{2}+4\left(\frac{x+1}{x}\right)+3=0 $$

Solve the equation by completing the square. \(x^{2}=\frac{3}{4} x-\frac{1}{8}\)

\(9- 46\) The given equation is either linear or equivalent to a linear equation. Solve the equation. $$ \frac{2 x-1}{x+2}=\frac{4}{5} $$

Solve the inequality. Express the answer using interval notation. $$ |x+1| \geq 1 $$

Value of Coins \(A\) 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?

\(9-32\) me solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ 2 \leq x+5<4 $$

Evaluate the expression and write the result in the form \(a+b i .\) $$ (6+5 i)(2-3 i) $$

1–54 ? Find all real solutions of the equation. $$ \left(\frac{1}{x+1}\right)^{2}-2\left(\frac{1}{x+1}\right)-8=0 $$

Find all real solutions of the equation. \(x^{2}-2 x-15=0\)

\(9- 46\) The given equation is either linear or equivalent to a linear equation. Solve the equation. $$ \frac{2}{t+6}=\frac{3}{t-1} $$

Solve the inequality. Express the answer using interval notation. $$ |x+4| \leq 0 $$

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?

\(9-32\) me solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ 5 \leq 3 x-4 \leq 14 $$

Evaluate the expression and write the result in the form \(a+b i .\) $$ (-2+i)(3-7 i) $$

1–54 ? Find all real solutions of the equation. $$ \left(\frac{x}{x+2}\right)^{2}=\frac{4 x}{x+2}-4 $$

Find all real solutions of the equation. \(x^{2}+5 x-6=0\)

\(9- 46\) The given equation is either linear or equivalent to a linear equation. Solve the equation. $$ \frac{1}{t-1}+\frac{t}{3 t-2}=\frac{1}{3} $$

Solve the inequality. Express the answer using interval notation. $$ |x+5| \geq 2 $$

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

\(9-32\) me solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ -1<2 x-5<7 $$

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

1–54 ? Find all real solutions of the equation. $$ x^{4}-13 x^{2}+40=0 $$

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

\(9- 46\) The given equation is either linear or equivalent to a linear equation. Solve the equation. $$ r-2[1-3(2 r+4)]=61 $$

Solve the inequality. Express the answer using interval notation. $$ |x+1| \geq 3 $$

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?

\(9-32\) me solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ 1<3 x+4 \leq 16 $$

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

1–54 ? Find all real solutions of the equation. $$ x^{4}-5 x^{2}+4=0 $$

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

\(9- 46\) The given equation is either linear or equivalent to a linear equation. Solve the equation. $$ (t-4)^{2}=(t+4)^{2}+32 $$

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

Dimensions of a Lot A square plot of land has a building 60 \(\mathrm{ft}\) long and 40 \(\mathrm{ft}\) wide at one corner. The rest of the land outside the building forms a parking lot. If the parking lot has area \(12,000 \mathrm{ft}^{2},\) what are the dimensions of the entire plot of land?

\(9-32\) me solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ -2<8-2 x \leq-1 $$

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

1–54 ? Find all real solutions of the equation. $$ 2 x^{4}+4 x^{2}+1=0 $$

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