1. Equations & Inequalities

Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the denominator. I=Prt,for P (simple interest)

A rectangular soccer field is twice as long as it is wide. If the perimeter of the soccer field is 300 yards, what are its dimensions?

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. 7|5x| + 2 = 16

Solve each equation. -4(2x-6) +8x= 5x+24+x

You are choosing between two gyms. One gym offers membership for a fee of \$40 plus a monthly fee of \$25. The other offers membership for a fee of \$15 plus a monthly fee of \$30. After how many months will the total cost at each gym be the same? What will be the total cost for each gym?

Solve each problem. See Example 2. Two planes leave Los Angeles at the same time. One heads south to San Diego, while the other heads north to San Francisco. The San Diego plane flies 50 mph slower than the San Francisco plane. In 1/2 hr, the planes are 275 mi apart. What are their speeds?

What is an inconsistent equation? Give an example.

An automobile repair shop charged a customer \$1182, listing \$357 for parts and the remainder for labor. If the cost of labor is \$75 per hour, how many hours of labor did it take to repair the car?

Solve each equation. |3 - 2x | = |5 - 2x |

Work each problem. Round to the nearest tenth of a degree if necessary. Temperature of VenusVenus is the hottest planet, with a surface temperature of 867°F. What is this temperature in degrees Celsius? (Data from The World Almanac and Book of Facts.)

Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? V = (1/3)Bh for B

Solve each problem. See Example 2. At the 2008 Summer Olympics in Beijing, Usain Bolt set a new Olympic and world record in the 100-m dash with a time of 9.69 sec. If this pace could be maintained for an entire 26-mi marathon, what would his time be? How would this time compare to the fastest time for a marathon, which is 2 hr, 3 min, 23 sec, set in 2013? (Hint: 1 m ≈ 3.281 ft.) (Data from Sports Illustrated Almanac.)