Exercises: Rearrange Formulas to Highlight a Quantity of Interest

Solve $2x + 6 = 14$ for $x$.

The equation $ax = b$ is solved for $x$. Which expression gives $x$?

In the formula $A = \frac{1}{2}bh$, you want to solve for $h$. Which statement best describes how to treat $b$?

Ohm's Law: $V = IR$. Rearrange to solve for $R$. Then find $R$ when $V = 24$ volts and $I = 3$ amps. Give your answer in ohms.

Distance formula: $d = rt$. Rearrange to solve for $t$. Then find $t$ when $d = 180$ miles and $r = 60$ miles per hour. Give your answer in hours.

Perimeter of a rectangle: $P = 2l + 2w$. Rearrange to solve for $w$. Then find $w$ when $P = 36$ cm and $l = 11$ cm. Give your answer in centimetres.

Area of a circle: $A = \pi r^2$. Rearrange to solve for $r$ (take the positive root). Then find $r$ when $A = 100\pi$ cm². Give your answer in centimetres.

Simple interest total: $A = P + Prt$, where $P$ is the principal, $r$ is the annual rate, and $t$ is time in years. Which expression correctly gives $P$ in terms of $A$, $r$, and $t$?