Course 2

Solving Multiplication Equations

Objectives

Review vocabulary Review solving equations by adding

or subtracting Solve multiplication equations using

Algebra tiles and paper and pencil Solve practical problems

Review

Use the following to answer the questions:

6x + 5 – 3y = 12

Is it an equation, expression or an inequality? How do you know?

Identify the term(s). Identify the variable(s). Identify the constant(s). Identify the coefficient(s).

Equation, it has an equals sign

6x, 5, 3y and 12

x and y

5 and 12

6 and -3

Review

Remember: Equations must be in balance, like a scale.

How would you solve this equation? x – 4 = 12

Use the opposite operation to undo the subtraction. x – 4 + 4 = 12 + 4 x = 16

Let’s look at how to solve an a multiplication equation.

Division Property of Equality

If you divide each side of an equation by the same nonzero number, the two sides remain equal.

Let’s Try It!

1) 2x = -8

What is the coefficient in this equation?

What is the opposite (inverse) of multiplying by 2?

2

Dividing by 2

2x = -8

Use the division property of equality: Divide both sides of the equation

by 22x = -82x = -8

2 2 x = -4

2x = -8

Check: 2x = -8

Replace the variable with the solution:

2(-4) = -8 -8 = -8

2) -5m = 40

What is the coefficient in this equation?

What is the opposite (inverse) of multiplying by -5?

Divide both sides of the equation by -5? -5m = 40 -5m = 40 -5 -5

m = -8

-5

Dividing by -5

-5m = 40

Check -5m = 40

Replace the variable with the solution:

-5(-8) = 40 40 = 40

3) 30 = 6n

What is the coefficient in this equation?

What is the opposite (inverse) of multiplying by 6?

Divide both sides of the equation by 6. 30 = 6n 30 = 6n

6 6 5 = n

6

Dividing by 6

30 = 6n

Check 30 = 6n

Replace the variable with the solution:

30 = 6(5) 30 = 30

4) 1.2x = -4.8

What is the coefficient in this equation?

What is the opposite (inverse) of multiplying by 1.2?

Divide both sides of the equation by 1.2. 1.2x = -4.8 1.2x = -4.8

1.2 1.2 x = -4

1.2

Dividing by 1.2

1.2x = -4.8

Check 1.2x = -4.8

Replace the variable with the solution:

1.2(-4) = -4.8 -4.8 = -4.8

5) -3y = 2

What is the coefficient in this equation? What is the opposite (inverse) of

multiplying by -3? Divide both sides of the equation by -3.

-3y = 2 -3y = 2

-3 -3 y =

3

2

Dividing by -3

-3

-3y = 2

Check -3y = 2

Replace the variable with the solution:

-3( ) = 2 2 = 2

3

2

Using an Equation to Solve a Problem

1) Sarah earns $5 per hour when she baby-sits. How many hours does she need to work to earn $75?

Write an equation: 5h = 75

Solve the equation: 5h = 75 5 5h = 15

Sarah must work 15 hours to earn $75.00.

Using an Equation to Solve a Problem.

2) A 125 pound person uses 4.4 calories per minute when walking. How many minutes will it take this person to use 44 calories?

Write an equation: 4.4m = 44

Solve the equation: 4.4m = 44 4.4 4.4m = 10

A 125 pound person must walk for 10 minutes to use 44 calories.