Math CentralQuandaries & Queries


Question from Paul, a student:

S=4wl+2wh and solve for h

Hi Paul,

You want to manipulate this equation to end with

\[h = \mbox{ some expression that doesn't involve h. }\]

The allowable manipulations are to add the same amount to each side of the equation or multiply each side of the equation by the same amount.

My first step would be to add $-4wl$ to each side of $S=4wl+2wh$ to get

\[S - 4wl =4wl+2wh - 4wl = 2wh.\]

At this point I would multiply each side of the equation by $\large \frac{1}{2w}$ to get

\[\frac{1}{2w} (S - 4wl) = \frac{1}{2w} 2wh = h.\]

It is conventional to write this expression with the $h$ term on the left side so I get

\[h = \frac{S - 4 wl}{2w}.\]


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