Rearrange formulas to isolate a chosen quantity and interpret the result.
Rearrange a formula by clearing a fraction or denominator to isolate a variable
Problem
Rearrange \(y~=~(1/2)x~+~b\) to solve for \(x\).
Big Picture
What this problem is really about
The fraction here is a coefficient multiplying the target, not a denominator containing the target. We’ll first remove the added constant, then multiply the entire remaining side by the reciprocal of that coefficient. Keeping the difference grouped is essential, and substitution will verify that the reciprocal cancels correctly across the whole expression.
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