Goal:

Let's solve multiplication equations

Solving an Equation

When we solve an equation, we find the value for the variable that makes the equal sign "true."

Basic Principle of Equality

In order to respect the equal sign in an equation, whatever operation we perform on one side of the equation, we need to perform the same action on the other side of the equal sign too.  In this way, the equation stays "equal."

Inverse Operations

Inverse operations "undo" one another.  Multiplication and division are inverse operations.

Example

Solve for x.

2x = 8

Using a Model

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Example

Solve for x.

 6x = 30

Using Inverse Operations

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Think --

• I need to get x by itself on one side of the equal sign.
• Right now x is being multiplied by 6.
• The inverse operation of multiplication is division.
• If I divide both sides by 6, I will solve the equation.

Solve --

Another Example (Solving a Division Equation)

Solve for x.

 = 0.5 

Think --

• I need to get x by itself on one side of the equal sign.
• Right now x is being divided by 4.
• The inverse operation of division is multiplication.
• If I multiply both sides by 4, I will solve the equation.

Solve --

    = 0.5            Write the original equation.

4 ·= 0.5 · 4      Multiply each side by 4.

    x = 2                Simplify.

Practice