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Solving One-Step Multiplication Equations

Oct 1, 2025

Overview

This lecture explains how to solve one-step multiplication equations by isolating the variable using the inverse operation, division.

Solving One-Step Multiplication Equations

  • The goal is to isolate the variable (get it alone on one side of the equation).
  • Undo the multiplication by using the inverse operation, which is division.
  • Always perform the same operation on both sides of the equation to keep it balanced.

Example 1: 8x = 72

  • "8x" means 8 multiplied by x.
  • To isolate x, divide both sides by 8: 8x ÷ 8 = 72 ÷ 8.
  • 8 ÷ 8 cancels to 1, leaving x alone: x = 9.
  • Check by substituting: 8 × 9 = 72, which is correct.

Example 2: 39 = 13w

  • "13w" means 13 times w.
  • To isolate w, divide both sides by 13: 39 ÷ 13 = 13w ÷ 13.
  • 13 ÷ 13 cancels to 1, leaving w alone: w = 3.
  • Check by substituting: 13 × 3 = 39, which is correct.
  • The variable can be written first: w = 3.

Key Terms & Definitions

  • Isolate the variable — Getting the variable alone on one side of the equation.
  • Inverse operation — The opposite operation; for multiplication, the inverse is division.
  • One-step equation — An equation that can be solved in a single step.

Action Items / Next Steps

  • Practice solving additional one-step multiplication equations.
  • Remember to check solutions by substituting them back into the original equations.