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.
Using the Addition Property of Equality
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?
