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.