# Solving One-Step Equations

## Lesson Preview

### What You'll Learn

- To solve equations using addition and subtraction
- To solve equations using multiplication and division

### … And Why

To model a geometric problem, as in Example 2

### Check Skills You'll Need

#### New Vocabulary

## Solving Equations Using Addition and Subtraction

An equation is like a balance scale because it shows that two quantities are equal. Look at the scales and equations below. The scales remain balanced when the same weight is added to each side.

Similarly, the scales remain balanced when the same weight is taken away from each side. This demonstrates the addition and subtraction properties of equality.

### Key Concepts

#### Property Addition Property of Equality

For every real number *a*, *b*, and *c*, if *a* = *b*, then *a* + *c* = *b* + *c*.

**Example** 8 = 5 + 3, so 8 + 4 = 5 + 3 + 4.

#### Property Subtraction Property of Equality

For every real number *a*, *b*, and *c*, if *a* = *b*, then *a* – c = *b* – c.

**Example** 8 = 5 + 3, so 8 – 2 = 5 + 3 – 2.

To solve an equation containing a variable, you find the value (or values) of the variable that make the equation true. Such a value is a solution of the equation. To find a solution, you can use properties of equality to form equivalent equations. Equivalent equations are equations that have the same solution (or solutions).

One way to solve an equation is to get the variable alone on one side of the equal sign. You can do this using inverse operations, which are operations that undo one another. Addition and subtraction are inverse operations.

##### Reading Math

The word *equivalent* is related to the word *equal*.

When you solve an equation involving addition, subtract the same number from each side of the equation.

##### Reading Math

represents a segment with endpoints *A* and *B*. *AB* represents the length of .

#### Using the Subtraction Property of Equality

GeometryThe triangle below is isosceles with sides and congruent. Find the value of *a*.

You can write and solve equations describing real-world situations. Use estimation to check whether your solution is reasonable.

#### Real-World Connection

Weighing a BabyA mother holds her baby and steps on a scale. The scale reading is 147 lb. Alone, the mother weighs 129 lb. How much does the baby weigh?