Chapter 1

Solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ 5-3 x \leq-16 $$

Solve the equation by factoring. $$ 6 x(x-1)=21-x $$

\(5-60\) Find all real solutions of the equation. $$ 2 x^{3}+x^{2}-18 x-9=0 $$

\(7-18 \cdot\) Express the given quantity in terms of the indicated variable. The time (in hours) it takes to travel a given distance at \(55 \mathrm{mi} / \mathrm{h} ; \quad d=\) given distance (in mi)

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

Evaluate the expression and write the result in the form a bi. $$ (-6+6 i)+(9-i) $$

\(5-22=\) Solve the equation. $$ 3|x+5|+6=15 $$

Solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ 2 x+1<0 $$

Solve the equation by completing the square. $$ x^{2}+2 x-5=0 $$

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

\(7-18 \cdot\) Express the given quantity in terms of the indicated variable. The concentration (in oz/gal) of salt in a mixture of 3 gal of brine containing 25 oz of salt to which some pure water has been added; \(x=\) volume of pure water added (in gal)

The given equation is either linear or equivalent to a linear equation. Solve the equation. \(x-3=2 x+6\)

Evaluate the expression and write the result in the form a bi. $$ (3-2 i)+\left(-5-\frac{1}{1} i\right) $$

\(5-22=\) Solve the equation. $$ 20+|2 x-4|=15 $$

Solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ 0<5-2 x $$

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

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

\(7-18 \cdot\) Express the given quantity in terms of the indicated variable. The value (in cents) of the change in a purse that contains twice as many nickels as pennies, four more dimes than nickels, and as many quarters as dimes and nickels combined; \(p=\) number of pennies

The given equation is either linear or equivalent to a linear equation. Solve the equation. \(4 x+7=9 x-13\)

Evaluate the expression and write the result in the form a bi. $$ (7-t i)-\left(5+\frac{1}{2} i\right) $$

\(5-22=\) Solve the equation. $$ 8+5\left|\frac{1}{3} X-\frac{5}{6}\right|=33 $$

Solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ 3 x+11 \leq 6 x+8 $$

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

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

Renting a Truck A rental company charges \(\$ 65\) a day and 20 cents a mile for renting a truck. Michel rents a truck for 3 days, and his bill comes to \(\$ 275 .\) How many miles did he drive?

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

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

\(5-22=\) Solve the equation. $$ \left|\frac{3}{5} x+2\right|-\frac{1}{2}=4 $$

Solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ 6-x \geq 2 x+9 $$

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

\(5-60\) Find all real solutions of the equation. $$ \frac{10}{x}-\frac{12}{x-3}+4=0 $$

Cell Phone Costs A cell phone company charges a monthly fee of \(\$ 10\) for the first 1000 text messages and 10 cents for each additional text message. Miriam's bill for text messages for the month of June is \(\$ 38.50 .\) How many text messages did she send that month?

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

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

\(5-22=\) Solve the equation. $$ |x-1|=|3 x+2| $$

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

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

\(5-60\) Find all real solutions of the equation. $$ \frac{x^{2}}{x+100}=50 $$

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

Investments Phyllis invested \(\$ 12,000,\) a portion earning a simple interest rate of 4\(\frac{1}{2} \%\) per year and the rest earning a rate of 4\(\%\) per year. After 1 year the total interest earned on these investments was \(\$ 525 .\) How much money did she invest at each rate?

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

\(5-22=\) Solve the equation. $$ |x+3|=|2 x+1| $$

Solve the linear inequality. Express the solution using interval notation and graph the solution set. $$ \frac{2}{5} X+1<\frac{1}{5}-2 X $$

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

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

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

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?

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

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

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