Isolating quantities

These questions give a formula and ask you to rearrange it for a different letter. There is nothing new to learn: it is the same reverse-order undoing used to solve an equation, with letters standing where numbers usually sit.

The habit that makes this easy is treating every other letter as though it were a number. To get $h$ out of $A = \frac{1}{2}bh$, you would multiply by $2$ and divide by $b$ if $b$ were $5$, so do exactly that.

Work in reverse order of operations, undoing the outermost thing first. If the target letter is inside a square root, square both sides before anything else; if it is in a denominator, multiply up first.

When the target appears twice, the method changes: gather all its terms on one side, factor it out, then divide by the bracket.

A useful check is to substitute simple numbers into both the original and the rearranged version. If they disagree, the rearrangement is wrong.

Solve $A = \frac{1}{2}bh$ for $h$.
Multiply by $2$, then divide by $b$

Solve $v = \sqrt{2gh}$ for $h$.
Undo the square root first by squaring both sides

Solve $ax = bx + c$ for $x$.
Here $x$ appears twice, so collect and factor