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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

 

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