# Solving Linear Equations

## Solve Equations Using the Division and Multiplication Properties of Equality


### Solve Equations Using the Division and Multiplication Properties of Equality

We introduced the Multiplication and Division Properties of Equality in Solve Equations Using Integers; The Division Property of Equality and Solve Equations with Fractions. We modeled how these properties worked using envelopes and counters and then applied them to solving equations (See Solve Equations Using Integers; The Division Property of Equality). We restate them again here as we prepare to use these properties again.
When you divide or multiply both sides of an equation by the same quantity, you still have equality. 
Let’s review how these properties of equality can be applied in order to solve equations. Remember, the goal is to ‘undo’ the operation on the variable. In the example below the variable is multiplied by  so we will divide both sides by  to ‘undo’ the multiplication.
In the previous example, to ‘undo’ multiplication, we divided. How do you think we ‘undo’ division?

### Solve Equations That Need to be Simplified

Many equations start out more complicated than the ones we’ve just solved. First, we need to simplify both sides of the equation as much as possible

### Key Concepts

1. Division and Multiplication Properties of Equality

### Practice Makes Perfect

Solve Equations Using the Division and Multiplication Properties of Equality 
In the following exercises, solve each equation for the variable using the Division Property of Equality and check the solution.
In the following exercises, solve each equation for the variable using the Multiplication Property of Equality and check the solution.
Solve Equations That Need to be Simplified 
In the following exercises, solve the equation.

### Everyday Math


### Writing Exercises


### Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.



ⓑ After reviewing this checklist, what will you do to become confident for all objectives?
