Chapter 2

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 . $$ -2(x+6)+3(2 x-5)=3(x-4)+10 $$

Solve each equation. See Examples 9 and \(10 .\) \(3(2 x+5)=-18+9\)

An architect designs a rectangular flower garden such that the width is exactly two-thirds of the length. If 260 feet of antique picket fencing are to be used to enclose the garden, find the dimensions of the garden.

A 25 -foot wire is to be cut so that the longer piece is one foot longer than 5 times the length of the shorter piece. Find the length of each piece.

Solve each inequality. Write each answer using solution set notation. $$ 6 x<5 $$

Solve each equation. See Examples 6 and \(7 .\) $$ -5(4 y-3)+2=-20 y+17 $$

Solve each equation. Don't forget to first simplify each side of the equation, if possible. Check each solution. See Examples 5 through 7 . $$ -5(x+1)+4(2 x-3)=2(x+2)-8 $$

Solve each equation. See Examples 9 and \(10 .\) \(2(4 x+1)=-12+6\)

If the length of a rectangular parking lot is 10 meters less than twice its width, and the perimeter is 400 meters, find the length of the parking lot.

Currently, the two fastest trains are the Japanese Maglev and the French TGV. The sum of their fastest speeds is 718.2 miles per hour. If the speed of the Maglev is 3.8 mph faster than the speed of the TGV, find the speeds of each.

Solve each inequality. Write each answer using solution set notation. $$ -\frac{2}{3} y \leq 8 $$

Solve. $$ 13 x-3=14 x $$

Solve each equation. See Examples 9 and \(10 .\) \(2 x-5=20 x+4\)

A flower bed is in the shape of a triangle with one side twice the length of the shortest side, and the third side is 30 feet more than the length of the shortest side. Find the dimensions if the perimeter is 102 feet.

The Pentagon is the world's largest office building in terms of floor space. It has three times the amount of floor space as the Empire State Building. If the total floor space for these two buildings is approximately 8700 thousand square feet, find the floor space of each building.

Solve each inequality. Write each answer using solution set notation. $$ -\frac{3}{4} y \geq 9 $$

Solve. See Examples 1 through 7 $$ \frac{4(5-w)}{3}=-w $$

Solve. $$ 18 x-9=19 x $$

Solve each equation. See Examples 9 and \(10 .\) \(6 x-4=-2 x-10\)

The perimeter of a yield sign in the shape of an isosceles triangle is 22 feet. If the shortest side is 2 feet less than the other two sides, find the length of the shortest side.

Two angles are supplementary if their sum is \(180^{\circ} .\) The larger angle below measures eight degrees more than three times the measure of the smaller angle. If \(x\) represents the measure of the smaller angle and these two angles are supplementary, find the measure of each angle.

Solve each inequality. Write each answer using solution set notation. $$ 4(2 z+1)<4 $$

Solve. See Examples 1 through 7 $$ -3(2 t-5)+2 t=5 t-4 $$

Iceberg lettuce is grown and shipped to stores for about 40 cents a head, and consumers purchase it for about 70 cents a head. Find the percent increase.

Solve. $$ 5 b-0.7=6 b $$

Solve each equation. See Examples 9 and \(10 .\) \(2+14=-4(3 x-4)\)

The Cat is a high-speed catamaran auto ferry that operates between Bar Harbor, Maine, and Yarmouth, Nova Scotia. The Cat can make the trip in about \(2 \frac{1}{2}\) hours at a speed of \(55 \mathrm{mph}\). About how far apart are Bar Harbor and Yarmouth?

Solve each inequality. Write each answer using solution set notation. $$ 6(2-z) \geq 12 $$

Solve. See Examples 1 through 7 $$ -(4 a-7)-5 a=10+a $$

The lettuce consumption per capita in 1990 was 31.5 pounds, and in 2007 the consumption dropped to 29.5 pounds. Find the percent decrease.

Solve. $$ 9 x+5.5=10 x $$

Solve each equation. See Examples 9 and \(10 .\) \(8+4=-6(5 x-2)\)

A family is planning their vacation to Disney World. They will drive from a small town outside New Orleans, Louisiana, to Orlando, Florida, a distance of 700 miles. They plan to average a rate of \(55 \mathrm{mph}\). How long will this trip take?

The measures of the angles of a triangle are 3 consecutive even integers. Find the measure of each angle.

Solve each inequality. Write each answer using solution set notation. $$ 3 x-7<6 x+2 $$

Solve. See Examples 1 through 7 $$ 5 y+2(y-6)=4(y+1)-2 $$

A student at the University of New Orleans makes money by buying and selling used cars. Charles bought a used car and later sold it for a \(20 \%\) profit. If he sold it for \(\$ 4680,\) how much did Charles pay for the car?

Solve. $$ 3 x-6=2 x+5 $$

Solve each equation. See Examples 9 and \(10 .\) \(-6 y-3=-5 y-7\)

A quadrilateral is a polygon with 4 sides. The sum of the measures of the 4 angles in a quadrilateral is \(360^{\circ} .\) If the measures of the angles of a quadrilateral are consecutive odd integers, find the measures.

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

Solve. See Examples 1 through 7 $$ 9 x+3(x-4)=10(x-5)+7 $$

The number of registered vehicles on the road in the United States is constantly increasing. In \(2007,\) there were approximately 246 million registered vehicles. This represents a \(3 \%\) increase over \(2002 .\) How many registered vehicles were there in the United States in \(2002 ?\) Round to the nearest million. (Source: Federal Highway Administration)

Solve. $$ 7 y+2=6 y+2 $$

Solve each equation. See Examples 9 and \(10 .\) \(-17 z-4=-16 z-20\)

The sum of \(\frac{1}{5}\) and twice a number is equal to \(\frac{4}{5}\) subtracted from three times the number. Find the number.

Solve each inequality. Write each answer using solution set notation. $$ 5 x-7 x \leq x+2 $$

By doubling each dimension, the area of a parallelogram increased from 36 square centimeters to 144 square centimeters. Find the percent increase in area.

Solve. $$ 13 x-9+2 x-5=12 x-1+2 x $$

Solve each equation. See Examples 9 and \(10 .\) \(\frac{1}{2}(2 x-1)=-\frac{1}{7}-\frac{3}{7}\)