SOL 7.14: Solving Equations By Multiplying Or Dividing
What is the inverse of multiplying? ______
Therefore, to get rid of a whole number or decimal that is stuck to the variable, divide both sides by that number.
What is the inverse of dividing? ______
Therefore, to get rid of a number that is being divided into the variable, multiply both sides by that number.
Example 1: Solve the equation and check your solution. Graph
the solution on a number line.
SOLVE / CHECK / GRAPH4x = 28
R = -3
7
Solve each equation in the table. Check your solutions. Graph the solutions on a number line.
SOLVE / CHECK / GRAPH1.8x = 72
-2t = 18
-64 = -4m
SOLVE / CHECK / GRAPH
K = 72
3
M = 18
-4
-11 = N
-6
The next problems have coefficients that are fractions. Do NOT change the fractions to decimals. Remember that dividing is the same as “MULTIPLYING BY THE RECIPROCAL”.
⅓R = 5
⅜x = -12
-¾ K = -½
Write and solve an equation for each situation listed below. Be sure to show the check and graph for your solution.
a. The product of a number and 6 is -42.
b. The quotient of a number and -4 is 8.
c. When you divide a number by -5, the result is -2.
d. In the driest part of an Outback ranch, each cow needs about 40 acres for grazing. Write and solve an equation to find how many cows can graze on 720 acres of land.
e. In China there are about 400,000,000 people with bicycles. This number represents 1/3 of the total population. About how many people live in China? Write and solve an equation to find China’s total population.
1) The largest ranch in the world is in the Australian Outback. It is about 12,000 square miles, which is five times the size of the largest United States ranch. Write and solve an equation to find the size of the largest United States ranch. Then graph the solution.2) Each student needs 12 minutes to give a report. A class period is 48 minutes long. Write and solve an equation to determine the number of students who could give a report in one class period. Then graph the solution.
3) One pound of ground beef makes four hamburger patties. Write and solve an equation to determine how many pounds of beef are needed to make 36 hamburgers. Then graph the solution.
4) It takes one painter 24 days to paint a house. Write and solve an equation to find how many painters are needed to paint a house in 6 days. Then graph the solution.
5) 348 students need to eat lunch at one time. Write and solve an equation to determine how many tables are needed if 6 students can sit at each table. Then graph the solution.
6) Mark spent $143 on boxes of candy bars. If each box of candy bars was $13, how many boxes of candy bars did he buy? Write and solve an equation, then graph the solution.
7) Mt. Everest in Nepal is the world’s tallest mountain, about 29,000 feet high. It is twice as high as Mount Whitney in California. How high is Mount Whitney? Write and solve an equation, then graph the solution.
8) Bob Johnson, a pro football player, earned twice as much money this year as last year. This year he earned $1,700,000. How much did he earn last year? Write and solve an equation, then graph the solution.
9) The John Paul Jones Arena in Charlottesville seats 16,000 people. It has almost twice as many seats as University Hall. Approximately how many seats does University Hall have? Write and solve an equation, then graph the solution.
1) The largest ranch in the world is in the Australian Outback. It is about 12,000 square miles, which is five times the size of the largest United States ranch. Write and solve an equation to find the size of the largest United States ranch. Then graph the solution.
2) Each student needs 12 minutes to give a report. A class period is 48 minutes long. Write and solve an equation to determine the number of students who could give a report in one class period. Then graph the solution.
3) One pound of ground beef makes four hamburger patties. Write and solve an equation to determine how many pounds of beef are needed to make 36 hamburgers. Then graph the solution.
4) It takes one painter 24 days to paint a house. Write and solve an equation to find how many painters are needed to paint a house in 6 days. Then graph the solution.
5) 348 students need to eat lunch at one time. Write and solve an equation to determine how many tables are needed if 6 students can sit at each table. Then graph the solution.
6) Mark spent $143 on boxes of candy bars. If each box of candy bars was $13, how many boxes of candy bars did he buy? Write and solve an equation, then graph the solution.
7) Mt. Everest in Nepal is the world’s tallest mountain, about 29,000 feet high. It is twice as high as Mount Whitney in California. How high is Mount Whitney? Write and solve an equation, then graph the solution.
8) Bob Johnson, a pro football player, earned twice as much money this year as last year. This year he earned $1,700,000. How much did he earn last year? Write and solve an equation, then graph the solution.
10) The John Paul Jones Arena in Charlottesville seats 16,000 people. It has almost twice as many seats as University Hall. Approximately how many seats does University Hall have? Write and solve an equation, then graph the solution.