Linear Equations • Topic 5 of 6

Literal Equations

A literal equation contains several letters, and "solving" it means isolating one chosen variable in terms of the others — exactly the same balance moves as a numerical equation, just with symbols. To solve A = lw for w, divide both sides by l to get w = A/l. Treat every other letter as a known constant. This skill lets you rearrange formulas (the SAT loves "solve for the indicated variable") and is essential for substitution in systems. Work step by step, undoing operations in reverse order, and the symbols behave just like numbers.

✅ Solved examples

1. Solve A = lw for w.
Divide both sides by l: w = A/l.
2. Solve d = rt for t.
Divide both sides by r: t = d/r.
3. Solve y = mx + b for x.
Subtract b: y − b = mx; divide by m: x = (y − b)/m.
4. Solve P = 2l + 2w for l.
Subtract 2w: P − 2w = 2l; divide by 2: l = (P − 2w)/2.

✏️ Practice — try these, take hints as needed

1. Solve V = lwh for h.
Divide both sides by lw.
h = V/(lw).
—
h = V/(lw).
2. Solve C = 2πr for r.
Divide both sides by 2π.
r = C/(2π).
—
r = C/(2π).
3. Solve y = kx for k.
Divide both sides by x.
k = y/x.
—
k = y/x.
4. Solve ax + b = c for x.
Subtract b.
ax = c − b.
Divide by a.
x = (c − b)/a.
5. Solve A = (1/2)bh for h.
Multiply both sides by 2.
2A = bh.
Divide by b.
h = 2A/b.

📝 Topic test — 8 questions

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