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Section 2-1

Solving One-Step Equations



Objective 2

Solving Equations Using Multiplication and Division


Multiplication and division are inverse operations. When you multiply or divide to solve equations, you use the following properties.

a key enclosed in a circle

Key Concepts

Property    Multiplication Property of Equality

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

Example 6/2 = 3, so 6/2 bullet 2 = 3 bullet 2.

Property    Division Property of Equality

For every real number a, b, and c, with c not equal to sign 0, if a = b, then a/b = b/c .

Example 3 + 1 = 4, so (3+1)/2 = 4/2 .

Multiplication and division are inverse operations. When you solve an equation involving division, multiply each side of the equation by the same number.

Example 4 Using the Multiplication Property of Equality

Solve – r/4 = – 10.4.

solution to -r/4=-10.4
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In the next example, the coefficient of the variable is a fraction. You can use reciprocals to solve the equation.

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To review reciprocals, see Lesson 1-6.

Example 5 Using Reciprocals to Solve Equations

Solve 3/4 x = 9.

solution to 3/4x=9
check mark Check Understanding

When you solve an equation involving multiplication, divide each side of the equation by the same number.

Example 6 Using the Division Property of Equality

Solve 4c = – 96.

solution to 4c = -96
check mark Check Understanding

Exercises Click here to view the Exercises for this lesson.

Algebra 1 iText

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Chapter 2
Solving Equations

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