Chapter 2

Solve each equation. Check each solution. See Examples 1 through \(6 .\) \(\frac{3}{4} n=-15\)

Substitute the given values into each given formula and solve for the unknown variable. $$ V=\frac{1}{3} A h ; \quad V=45, h=5 $$

Solve. For Exercises 9 and \(10,\) the solutions have been started for you. A 25 -inch piece of steel is cut into three pieces \(s o\) that the second piece is twice as long as the first piece, and the third piece is one inch more than five times the length of the first piece. Find the lengths of the pieces

Graph each inequality on the number line. $$ -1 < x < 3 $$

Solve each equation. See Examples 1 and \(2 .\) $$ -6(x-3)-26=-8 $$

Solve each equation. Check each solution. $$ x-\frac{2}{5}=-\frac{3}{20} $$

Solve each equation. Check each solution. See Examples 1 through \(6 .\) \(\frac{1}{6} d=\frac{1}{2}\)

Substitute the given values into each given formula and solve for the unknown variable. $$ C=2 \pi r ; \quad C=15.7 $$

Solve the solutions have been started for you. A 46 -foot piece of rope is cut into three pieces so that the second piece is three times as long as the first piece, and the third piece is two feet more than seven times the length of the first piece. Find the lengths of the pieces.

Graph each inequality on the number line. $$ -2 \leq x \leq 3 $$

Solve each equation. See Examples 1 and \(2 .\) $$ -4(n-4)-23=-7 $$

Solve each equation. Check each solution. $$ y-\frac{4}{7}=-\frac{3}{14} $$

Solve each equation. Check each solution. See Examples 1 through \(6 .\) \(\frac{1}{8} v=\frac{1}{4}\)

Substitute the given values into each given formula and solve for the unknown variable. $$ A=\pi r^{2} ; \quad r=4 $$

A 40 -inch board is to be cut into three pieces so that the second piece is twice as long as the first piece and the third piece is 5 times as long as the first piece. If \(x\) represents the length of the first piece, find the lengths of all three pieces.

Graph each inequality on the number line. $$ 0 \leq y<2 $$

A used automobile dealership recently reduced the price of a used sports car by \(8 \%\). If the price of the car before discount was \(\$ 18,500,\) find the discount and the new price.

Solve each equation. Check each solution. $$ \frac{1}{3}+f=\frac{3}{4} $$

Solve each formula for the specified variable. \(f=5 g h\) for \(h\)

A 21 -foot beam is to be divided so that the longer piece is 1 foot more than 3 times the length of the shorter piece. If \(x\) represents the length of the shorter piece, find the lengths of both pieces.

Graph each inequality on the number line. $$ -4

A music store is advertising a \(25 \%\) -off sale on all new releases. Find the discount and the sale price of a newly released CD that regularly sells for \(\$ 12.50\).

Solve each equation. Check each solution. $$ c+\frac{1}{6}=\frac{3}{8} $$

Solve each formula for the specified variable. \(x=4 \pi y\) for \(y\)

In 2008 , New Mexico produced 15 million pounds more pecans than Texas. Together, the two states produced 75 million pounds of pecans. Find the amount of pecans grown in New Mexico and Texas in 2008\. (Source: National Agriculture Statistics Service)

Solve each inequality. Graph the solution set. Write each answer using solution set notation. $$ x-2 \geq-7 $$

A birthday celebration meal is \(\$ 40.50\) including tax. Find the total cost if a \(15 \%\) tip is added to the cost.

Solve each equation. See Examples 1 and \(2 .\) $$ 4 x+3=-3+2 x+14 $$

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 . $$ 7 x+2 x=8 x-3 $$

Solve each equation. Check each solution. See Examples 1 through \(6 .\) \(\frac{k}{-7}=0\)

Solve each formula for the specified variable. \(V=l w h\) for \(w\)

In the 2008 Summer Olympics, the U.S. team won 13 more gold medals than the Russian team. If the total number of gold medals won by both teams was \(59,\) find the number of gold medals won by each team. (Source: Beijing 2008 Olympic Games)

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

A retirement dinner for two is \(\$ 65.40\) including tax. Find the total cost if a \(20 \%\) tip is added to the cost.

Solve each equation. See Examples 1 and \(2 .\) $$ 6 y-8=-6+3 y+13 $$

$$ 3 n+2 n=7+4 n $$

Solve each equation. Check each solution. See Examples 1 through \(6 .\) \(\frac{f}{-5}=0\)

Solve each formula for the specified variable. \(T=m n r\) for \(n\)

A car rental agency advertised renting a Buick Century for \(\$ 24.95\) per day and \(\$ 0.29\) per mile. If you rent this car for 2 days, how many whole miles can you drive on a \(\$ 100\) budget?

Solve each inequality. Graph the solution set. Write each answer using solution set notation. $$ -9+y<0 $$

Solve. The number of fraud complaints for Internet auction sites decreased from 148,600 in 2005 to 73,900 in 2007 . Find the percent decrease. Round to the nearest whole percent. (Source: FBI)

Solve each equation. See Examples 1 and \(2 .\) $$ -2 y-10=5 y+18 $$

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 . $$ \frac{5}{6} x+\frac{1}{6} x=-9 $$

Solve each equation. Check each solution. See Examples 1 through \(6 .\) \(1.7 x=10.71\)

Solve each formula for the specified variable. \(3 x+y=7\) for \(y\)

A plumber gave an estimate for the renovation of a kitchen. Her hourly pay is \(\$ 27\) per hour and the plumbing parts will cost \(\$ 80 .\) If her total estimate is \(\$ 404\), how many hours does she expect this job to take?

Solve each inequality. Graph the solution set. Write each answer using solution set notation. $$ -3+m>5 $$

Solve. The number of text messages rose from 996 million in June to 1100 million in December. Find the percent increase. Round to the nearest whole percent.

Solve each equation. See Examples 1 and \(2 .\) $$ -7 n+5=8 n-10 $$

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 . $$ \frac{13}{11} y-\frac{2}{11} y=-3 $$