Example3.3.6

Solve for $$b$$ in $$A=\frac{1}{2}bh\text{.}$$ (This is the area formula for a triangle.)

To solve for $$b\text{,}$$ we need to determine what operations need to be “undone.” The expression $$\frac{1}{2}bh$$ has multiplication between $$\frac{1}{2}$$ and $$b$$ and $$h\text{.}$$ As a first step, we will multiply each side of the equation by $$2$$ in order to eliminate the denominator of $$2\text{:}$$

\begin{align*} A\amp=\frac{1}{2}\attention{b}h\\ \multiplyleft{2}A\amp=\multiplyleft{2}\frac{1}{2}\attention{b}h\\ 2A\amp=\attention{b}h \end{align*}

As a last step, we will “undo” the multiplication between $$b$$ and $$h$$ by dividing each side by $$h\text{:}$$

\begin{align*} \divideunder{2A}{h}\amp=\divideunder{\attention{b}h}{h}\\ \frac{2A}{h}\amp=\attention{b}\\ b\amp=\frac{2A}{h} \end{align*}
in-context