Overview
This lecture explains how to rearrange formulas to isolate a specific variable, using step-by-step algebraic manipulation.
Steps to Rearrange Formulas
- To isolate a variable, perform inverse operations to both sides of the equation.
- Mirror each operation as you would when solving standard equations.
Example 1: Make x the Subject in y = 3x + 4
- Subtract 4 from both sides: y - 4 = 3x.
- Divide both sides by 3: (y - 4)/3 = x.
- Rearranged formula: x = (y - 4)/3.
Example 2: Make b the Subject in a = b/3 - 5
- Add 5 to both sides: a + 5 = b/3.
- Multiply both sides by 3: 3(a + 5) = b.
- Expand: 3a + 15 = b.
- Rearranged formula: b = 3a + 15.
Example 3: Isolate x in 2y = 3(x + 2)
- Expand brackets: 2y = 3x + 6.
- Subtract 6: 2y - 6 = 3x.
- Divide by 3: (2y - 6)/3 = x.
- Rearranged formula: x = (2y - 6)/3.
Example 4: Isolate b in 6a - 3 = b/2 + 3
- Subtract 3: 6a - 3 = b/2.
- Multiply by 2: 2(6a - 3) = b.
- Expand: 12a - 6 = b.
- Rearranged formula: b = 12a - 6.
Key Terms & Definitions
- Subject of the equation — The variable isolated (by itself) on one side of the formula.
- Inverse operation — The opposite mathematical operation used to cancel out terms (e.g., subtraction cancels addition).
Action Items / Next Steps
- Practice rearranging similar formulas to isolate different variables.
- Review methods for expanding brackets and inverse operations.