Chapter 1

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

Solve the equation by completing the square. \(x^{2}-6 x-11=0\)

\(9- 46\) The given equation is either linear or equivalent to a linear equation. Solve the equation. $$ -7 w=15-2 w $$

Solve the equation. $$ \left|\frac{3}{5} x+2\right|-\frac{1}{2}=4 $$

Investments If Ben invests \(\$ 4000\) at 4\(\%\) interest per year, how much additional money must he invest at 5\(\frac{1}{2} \%\) annual interest to ensure that the interest he receives each year is 4\(\frac{1}{2} \%\) of the total amount invested?

\(9-32\) me solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ 0<5-2 x $$

Evaluate the expression and write the result in the form \(a+b i .\) $$ (-4+i)-(2-5 i) $$

1–54 ? Find all real solutions of the equation. $$ \frac{10}{x}-\frac{12}{x-3}+4=0 $$

Solve the equation by completing the square. \(x^{2}+3 x-\frac{7}{4}=0\)

\(9- 46\) The given equation is either linear or equivalent to a linear equation. Solve the equation. $$ 5 t-13=12-5 t $$

Solve the equation. $$ |x-1|=|3 x+2| $$

Salaries An executive in an engineering firm earns a monthly salary plus a Christmas bonus of \(\$ 8500\) . If she earns a total of \(\$ 97,300\) per year, what is her monthly salary?

\(9-32\) me solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ 3 x+11 \leq 6 x+8 $$

Evaluate the expression and write the result in the form \(a+b i .\) $$ (-12+8 i)-(7+4 i) $$

1–54 ? Find all real solutions of the equation. $$ \frac{x^{2}}{x+100}=50 $$

Solve the equation by completing the square. \(x^{2}+x-\frac{3}{4}=0\)

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

Solve the equation. $$ |x+3|=|2 x+1| $$

Salaries A woman earns 15\(\%\) more than her husband. Together they make \(\$ 69,875\) per year. What is the husband's annual salary?

\(9-32\) me solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ 6-x \geq 2 x+9 $$

Evaluate the expression and write the result in the form \(a+b i .\) $$ 6 i-(4-i) $$

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

Solve the equation by completing the square. \(x^{2}-5 x+1=0\)

\(9- 46\) The given equation is either linear or equivalent to a linear equation. Solve the equation. $$ \frac{z}{5}=\frac{3}{10} z+7 $$

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

Inheritance Craig is saving to buy a vacation home. He inherits some money from a wealthy uncle, then combines this with the \(\$ 22,000\) he has already saved and doubles the total in a lucky investment. He ends up with \(\$ 134,000\) , just enough to buy a cabin on the lake. How much did he inherit?

\(9-32\) me solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ \frac{1}{2} x-\frac{2}{3}>2 $$

Evaluate the expression and write the result in the form \(a+b i .\) $$ 4(-1+2 i) $$

1–54 ? Find all real solutions of the equation. $$ \frac{x+5}{x-2}=\frac{5}{x+2}+\frac{28}{x^{2}-4} $$

Solve the equation by completing the square. \(x^{2}+22 x+21=0\)

\(9- 46\) The given equation is either linear or equivalent to a linear equation. Solve the equation. $$ 2(1-x)=3(1+2 x)+5 $$

Solve the inequality. Express the answer using interval notation. $$ |3 x|<15 $$

Overtime Pay Helen earns \(\$ 7.50\) an hour at her job, but if she works more than 35 hours in a week she is paid 1\(\frac{1}{2}\) times her regular salary for the overtime hours worked. One week her gross pay was \(\$ 352.50 .\) How many overtime hours did she work that week?

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

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

1–54 ? Find all real solutions of the equation. $$ \frac{x}{2 x+7}-\frac{x+1}{x+3}=1 $$

Solve the equation by completing the square. \(x^{2}-18 x=19\)

\(9- 46\) The given equation is either linear or equivalent to a linear equation. Solve the equation. $$ 5(x+3)+9=-2(x-2)-1 $$

Solve the inequality. Express the answer using interval notation. $$ |2 x|>7 $$

Labor Costs A plumber and his assistant work together to replace the pipes in an old house. The plumber charges \(\$ 45\) an hour for his own labor and \(\$ 25\) an hour for his assistant's labor. The plumber works twice as long as his assistant on this job, and the labor charge on the final bill is \(\$ 4025 .\) How long did the plumber and his assistant work on this job?

\(9-32\) me solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ \frac{1}{3} x+2<\frac{1}{6} x-1 $$

Evaluate the expression and write the result in the form \(a+b i .\) $$ (7-i)(4+2 i) $$

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

Solve the equation by completing the square. \(2 x^{2}+8 x+1=0\)

\(9- 46\) The given equation is either linear or equivalent to a linear equation. Solve the equation. $$ 4\left(y-\frac{1}{2}\right)-y=6(5-y) $$

Solve the inequality. Express the answer using interval notation. $$ \frac{1}{2}|x| \geq 1 $$

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?

\(9-32\) me solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ \frac{2}{3}-\frac{1}{2} x \geq \frac{1}{6}+x $$

Evaluate the expression and write the result in the form \(a+b i .\) $$ (5-3 i)(1+i) $$

1–54 ? Find all real solutions of the equation. $$ \frac{x+\frac{2}{x}}{3+\frac{4}{x}}=5 x $$