Digits, Grade 7, Volume 1, Homework Helper

# Unit B: Expressions, Equations, and Relationships

## Topic 2: Equations & Inequalities

### 2-1: Solving Simple Equations

#### Key Concept

You can think of solving an equation as transforming the equation into a simpler equivalent equation. Your goal is to use inverse operations and the Properties of Equality to isolate the variable on one side of the equal sign.

Addition Property of Equality If you add the same number to each side of an equation, the two sides remain equal.

table with 4 rows and 2 columns , row1 column 1 , . cap arithmetic , column 2 , cap algebra , row2 column 1 , 6 equals 3 open 2 close , column 2 cap if eh equals b comma , then , row3 column 1 , 6 plus 5 equals 3 open 2 close plus 5 , column 2 eh plus c equals b plus c , row4 column 1 , 11 equals 11 , column 2 forallnumbers . eh comma b , commaand , c . , end table

Subtraction Property of Equality If you subtract the same number from each side of an equation, the two sides remain equal.

table with 4 rows and 2 columns , row1 column 1 , . cap arithmetic , column 2 , cap algebra , row2 column 1 , 9 equals 3 open 3 close , column 2 cap if eh equals b comma , then , row3 column 1 , 9 minus 2.5 equals 3 open 3 close minus 2.5 , column 2 eh minus c equals b minus c , row4 column 1 , 6.5 equals 6.5 , column 2 forallnumbers . eh comma b , commaand , c . , end table

#### Part 1

Intro

You can think of an equation as a balanced scale. When you do something to one side of an equation, you must do the same thing to the other side to keep it balanced.