Lines and Slope

Literal Equations

Solve a formula for a specified variable by applying inverse operations to both sides. Each step is a valid algebraic operation that preserves the equation's truth — the rearrangement is equivalent to the original.

Example

Solve a formula for a named variable using inverse operations.

highlighted = computed this step

Step 1 — Set up

Set up the expression.

A=12bhA=\frac{ 1 }{ 2 }bh
Target h: isolate h in the formula.A = (1/2) · b · htarget hclear the 1/2--then isolate h--

Step 2 — Multiply by denominator

Multiply both sides by 2.

2A=bh\hl{2} A=bh
Multiply both sides by 2 to remove 1/2.A = (1/2) · b · htarget hmultiply both sides by 22A = b · hthen isolate h--

Step 3 — Divide by b

Divide by b to isolate h with 2A over b.

h=2Abh=\frac{ \hl{2} A}{b}
Divide both sides by b to isolate h.A = (1/2) · b · htarget hmultiply both sides by 22A = b · hdivide both sides by bh = 2A / b
literal-equations To solve A = (1/2)·b·h for h: multiply both sides by 2, then divide both sides by b. The result h = 2A/b can be verified by substituting back into the original formula.