Linear Equations • Topic 6 of 6

Formula Rearrangement

Rearranging a formula is solving a literal equation in a real-world context — making a different quantity the subject. The same rules apply: undo operations in reverse, keeping both sides balanced, and treat the other variables as constants. For the temperature formula F = (9/5)C + 32, to solve for C you subtract 32 and multiply by 5/9. Being able to rearrange means you can plug numbers into whichever form a question needs. On the SAT this appears as "which equation correctly expresses … in terms of …", testing clean algebraic manipulation rather than arithmetic.

✅ Solved examples

1. Rearrange F = (9/5)C + 32 to solve for C.
Subtract 32: F − 32 = (9/5)C; multiply by 5/9: C = (5/9)(F − 32).
2. Rearrange v = u + at to solve for a.
Subtract u: v − u = at; divide by t: a = (v − u)/t.
3. Rearrange E = mc² to solve for m.
Divide both sides by c²: m = E/c².
4. Rearrange A = P(1 + r) to solve for r.
Divide by P: A/P = 1 + r; subtract 1: r = A/P − 1.

✏️ Practice — try these, take hints as needed

1. Rearrange y = mx + b to solve for b.
Subtract mx from both sides.
b = y − mx.
—
b = y − mx.
2. Rearrange P = IV to solve for I.
Divide both sides by V.
I = P/V.
—
I = P/V.
3. Rearrange s = (1/2)gt² to solve for g.
Multiply both sides by 2.
2s = gt².
Divide by t².
g = 2s/t².
4. Rearrange d = rt to solve for r.
Divide both sides by t.
r = d/t.
—
r = d/t.
5. Rearrange y − y₁ = m(x − x₁) to solve for m.
Divide both sides by (x − x₁).
m = (y − y₁)/(x − x₁).
—
m = (y − y₁)/(x − x₁).

📝 Topic test — 8 questions

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