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All courses Algebra II · A-CED.4 18 of 55
Rearrange formulas to highlight a chosen quantity across the expression types studied.

Rearrange a formula to isolate a linear target variable in one term

Problem
Rearrange \(A~=~lw\) to isolate \(l\), including any required condition.
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Hint

Divide both sides by the factor attached to \(l\).

In a product formula like \(A=lw\), isolate one variable by dividing by the other factor, as long as that factor is not \(0\).

Solution walkthrough

01

Identify the factor multiplying the target

\[A=l*w\]

In the area formula, the target variable l is multiplied by w.

02

Use the inverse operation

\[A/w=l\]

Dividing both sides by w undoes multiplication by w and isolates l.

03

State the required condition

\[w\ne~0\]

The rearrangement divides by w, so it is valid only when w is nonzero.

04

Write the isolated formula

\[l~=~A/w,~w~\ne~0\]

Reordering the equality gives l=A/w with the necessary condition w!=0, choice A.

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Another way

  1. Use the multiplication fact family: if A=l*w and w is nonzero, then the missing factor l equals product A divided by factor w.

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Common mistake

Do not divide by l when l is the quantity being isolated. Undo its multiplication by dividing both sides by the other factor w.

Solution walkthrough video