Chapter 2

Solve each formula for the specified variable. \(-x+y=13\) for \(y\)

In one U.S. city, the taxi cost is \(\$ 3\) plus \(\$ 0.80\) per mile. If you are traveling from the airport, there is an additional charge of \(\$ 4.50\) for tolls. How far can you travel from the airport by taxi for \(\$ 27.50 ?\)

Solve each inequality. Graph the solution set. Write each answer using solution set notation. $$ 3 x-5>2 x-8 $$

Solve.By decreasing each dimension by 1 unit, the area of a rectangle decreased from 40 square feet (on the left) to 28 square feet (on the right). Find the percent decrease in area.

Solve each equation. See Examples 3 through \(5 .\) $$ \frac{2}{3} x+\frac{4}{3}=-\frac{2}{3} $$

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 . $$ 2 y+10=5 y-4 y $$

Solve each equation. Check each solution. See Examples 7 and 8 . \(2 x-4=16\)

Solve each formula for the specified variable. \(A=P+P R T\) for \(R\)

A professional carpet cleaning service charges \(\$ 30\) plus \(\$ 25.50\) per hour to come to your home. If your total bill from this company is \(\$ 119.25\) before taxes, for how many hours were you charged?

Solve each inequality. Graph the solution set. Write each answer using solution set notation. $$ 3-7 x \geq 10-8 x $$

Solve.By decreasing the length of the side by one unit, the area of a square decreased from 100 square meters to 81 square meters. Find the percent decrease in area.

Solve each equation. See Examples 3 through \(5 .\) $$ \frac{4}{5} x-\frac{8}{5}=-\frac{16}{5} $$

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 . $$ 4 x-4=10 x-7 x $$

Solve each equation. Check each solution. See Examples 7 and 8 . \(3 x-1=26\)

Solve each formula for the specified variable. \(A=P+P R T\) for \(T\)

The flag of Equatorial Guinea contains an isosceles triangle. (Recall that an isosceles triangle contains two angles with the same measure.) If the measure of the third angle of the triangle is \(30^{\circ}\) more than twice the measure of either of the other two angles, find the measure of each angle of the triangle. (Hint: Recall that the sum of the measures of the angles of a triangle is \(180^{\circ} .\) )

Solve each inequality. Graph the solution set. Write each answer using solution set notation. $$ 4 x-1 \leq 5 x-2 x $$

Solve.Find the original price of a pair of shoes if the sale price is \(\$ 78\) after a \(25 \%\) discount.

Solve each equation. See Examples 3 through \(5 .\) $$ \frac{3}{4} x-\frac{1}{2}=1 $$

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 . $$ -5(n-2)=8-4 n $$

Solve each formula for the specified variable. \(V=\frac{1}{3} A h\) for \(A\)

The flag of Brazil contains a parallelogram. One angle of the parallelogram is \(15^{\circ}\) less than twice the measure of the angle next to it. Find the measure of each angle of the parallelogram. (Hint: Recall that opposite angles of a parallelogram have the same measure and that the sum of the measures of the angles is \(360^{\circ} .\) )

Solve each inequality. Graph the solution set. Write each answer using solution set notation. $$ 7 x+3<9 x-3 x $$

Solve.Find the original price of a popular pair of shoes if the increased price is \(\$ 80\) after a \(25 \%\) increase.

Solve each equation. See Examples 3 through \(5 .\) $$ \frac{2}{9} x-\frac{1}{3}=1 $$

Solve each formula for the specified variable. \(D=\frac{1}{4} f k\) for \(k\)

The sum of the measures of the angles of a parallelogram is \(360^{\circ} .\) In the parallelogram below, angles \(A\) and \(D\) have the same measure as well as angles \(C\) and \(B\). If the measure of angle \(C\) is twice the measure of angle \(A,\) find the measure of each angle.

Solve each inequality. Graph the solution set. $$ 2 x<-6 $$

Solve each equation. See Examples 3 through \(5 .\) $$ 0.50 x+0.15(70)=35.5 $$

Solve.Find last year's salary if after a \(4 \%\) pay raise, this year's salary is \(\$ 44,200\).

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 . $$ \frac{3}{7} x+2=-\frac{4}{7} x-5 $$

Solve each formula for the specified variable. \(P=a+b+c\) for \(a\)

Solve each inequality. Graph the solution set. $$ 3 x>-9 $$

Solve each equation. See Examples 3 through \(5 .\) $$ 0.40 x+0.06(30)=9.8 $$

Solve.Find last year's salary if after a \(3 \%\) pay raise, this year's salary is \(\$ 55,620\).

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 . $$ \frac{1}{5} x-1=-\frac{4}{5} x-13 $$

Solve each equation. Check each solution. See Examples 7 and 8 . \(8 t+5=5\)

Solve each formula for the specified variable. \(P R=x+y+z+w\) for \(z\)

Solve each inequality. Graph the solution set. $$ -8 x \leq 16 $$

Solve each equation. See Examples 3 through \(5 .\) $$ \frac{2(x+1)}{4}=3 x-2 $$

Solve. For each exercise, a table is given for you to complete and use to write an equation that models the situation. How much pure acid should be mixed with 2 gallons of a \(40 \%\) acid solution in order to get a \(70 \%\) acid solution?

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 . $$ 5 x-6=6 x-5 $$

Solve each formula for the specified variable. \(S=2 \pi r h+2 \pi r^{2}\) for \(h\)

Solve each inequality. Graph the solution set. $$ -5 x<20 $$

Solve each equation. See Examples 3 through \(5 .\) $$ \frac{3(y+3)}{5}=2 y+6 $$

Solve. For each exercise, a table is given for you to complete and use to write an equation that models the situation. How many cubic centimeters \((\mathrm{cc})\) of a \(25 \%\) antibiotic solution should be added to 10 cubic centimeters of a \(60 \%\) antibiotic solution in order to get a \(30 \%\) antibiotic solution?

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 . $$ 2 x+7=x-10 $$

Solve each equation. Check each solution. See Examples 7 and 8 . \(\frac{b}{4}-1=-7\)

Solve each formula for the specified variable. \(S=4 l w+2 w h\) for \(h\)

Solve each inequality. Graph the solution set. $$ -x>0 $$