# 1.6 – Solving Equations with Multiplication and Division

Objectives

• Reverse the operation found in an equation to isolate variables from constants.
• Solve equations involving multiplication and division by mapping them on the number line.
• Ask the questions necessary to turn real-life problems into mathematical sentences.

(No Key Terms)

Notes

• Standard Form
• Multiplication
• $ax=b$
• Division
• $\frac{x}{a}=b$

•  Coefficient
• The number that is multiplied by a variable
• The number that goes WITH a variable
• Examples:
• 6x: Coefficient is 6
• -18a: Coefficient is -18
• 55d: Coefficient is 55

• Reverse Operations (opposites)
• Multiplication / Division are reverse operations
• Addition / Subtraction are reverse operations
• Squares / Square Roots are reverse operations

• To solve for (or isolate) any variable:
• 1. Combine like terms on the left side of the equation or inequality and on then on the right side
• 2. Perform the reverse operation on any constant terms first (cancel out these terms)
• 3. Perform the reverse operation on the coefficient terms first (cancel out these terms)
• Example 1:
• 3x + 2 – x = 7 + 2
• 1. 2x + 2 = 9 (combined 3x and -x on the left, then combined 7 + 2 on the right)
• 2. 2x = 7 (subtracted 2 on both sides)
• 3. x = 7/2 (divided both sides by 2)
• Example 2:
• $\frac{x}{9}=3$ (this is a fraction problem, which is division)
• 1. What is the reverse operation of division?  Answer: multiplication
• 2. Multiply both sides by 9
• 3. Answer:  x = 27