Chapter 1

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

\(5-60\) Find all real solutions of the equation. $$ \frac{x+5}{x-2}=\frac{5}{x+2}+\frac{28}{x^{2}-4} $$

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

Investments What annual rate of interest would you have to earn on an investment of \(\$ 3500\) to ensure receiving \(\$ 262.50\) interest after 1 year?

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

\(23-48\) Solve the inequality. Express the answer using interval notation. $$ |3 x|<15 $$

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

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

\(5-60\) Find all real solutions of the equation. $$ \frac{x}{2 x+7}-\frac{x+1}{x+3}=1 $$

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

Investments Jack invests \(\$ 1000\) at a certain annual interest rate, and he invests another \(\$ 2000\) at an annual rate that is one-half percent higher. If he receives a total of \(\$ 190\) interest in 1 year, at what rate is the \(\$ 1000\) invested?

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

\(23-48\) Solve the inequality. Express the answer using interval notation. $$ |2 x|>7 $$

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

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

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

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

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?

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

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

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

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

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

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

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

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

\(23-48\) Solve the inequality. Express the answer using interval notation. $$ |x-5| \leq 3 $$

Solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ 2 \leq x+5<4 $$

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

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

The given equation is either linear or equivalent to a linear equation. Solve the equation. \(X-\frac{1}{3} X-\frac{1}{2} X-5=0\)

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?

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

\(23-48\) Solve the inequality. Express the answer using interval notation. $$ |x-9|>9 $$

Solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ 5 \leq 3 x-4 \leq 14 $$

Solve the equation by completing the square. $$ X^{2}=\frac{3}{4} X-\frac{1}{8} $$

\(5-60\) Find all real solutions of the equation. $$ \sqrt{4-6 x}=2 x $$

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

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?

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

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

Solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ -1<2 x-5<7 $$

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

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

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

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?

\(23-48\) Solve the inequality. Express the answer using interval notation. $$ |x+4| \leq 0 $$

Solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ 1<3 x+4 \leq 16 $$

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

\(5-60\) Find all real solutions of the equation. $$ x-\sqrt{9-3 x}=0 $$