SAT Topic 6

Rearranging formulas

Solve for one variable in terms of the others — the SAT loves "which expression equals x?"

Concept

Rearranging a formula is the same skill as solving a linear equation, with one mental switch: treat every letter except your target as a constant. Don't let the unfamiliar symbols throw you off.

Identify the target. The variable you want isolated.
Undo the outermost operation first. If the target is wrapped inside parentheses or sitting in a numerator, peel back layer by layer.
Factor when needed. If the target appears in two different terms, group them on one side and factor it out.

Cross-check by plugging numbers into both the original and your rearranged version — they should produce the same value.

Worked example 1

Temperature conversion: `C = (5/9)(F − 32)`. Solve for F.

Solution

Step 1. Multiply both sides by 95 to peel off the fraction: (9/5)C = F − 32

Step 2. Add 32 to both sides: F = (9/5)C + 32

F = (9/5)C + 32. Check at C = 0: F = 0 + 32 = 32 — the freezing point of water in °F. ✓

Worked example 2

Trapezoid area: `A = ½(b₁ + b₂)h`. Solve for b₁.

Solution

Step 1. Multiply both sides by 2 to clear the half: 2A = (b₁ + b₂)h

Step 2. Divide both sides by h: 2A / h = b₁ + b₂

Step 3. Subtract b₂: b₁ = 2A/h − b₂

b₁ = 2A/h − b₂. Note how b₂, A, and h are all just constants from b₁'s point of view.

Practice test

8 questions on isolating a chosen variable. Includes geometry formulas, conversion formulas, and "equivalent expression" problems.

Practice test · 8 questions Question 1 of 8 · Score 0