Integrated Math 1 / Unit 2: Equations and Inequalities
2.2 Literal Equations and Formulas
Notes
A literal equation has several variables. To solve for one variable, treat the others as numbers and use inverse operations.
- Solve $y = mx + b$ for $m$: $y - b = mx$, so $\displaystyle m = \frac{y - b}{x}$.
- Whatever you do to one side, do to the whole other side.
- Example: solve $d = rt$ for $t$: $\displaystyle t = \frac{d}{r}$.
- Divide every term when you divide, not just one.
Practice
Solve $y = mx + b$ for $m$.
Subtract $b$ from both sides, then divide by $x$.
Solve $\displaystyle C = \frac{5}{9}(F - 32)$ for $F$.
Multiply by $\displaystyle \frac{9}{5}$: $\displaystyle \frac{9}{5}C = F - 32$. Then add 32.
Solve $3x + 2y = 12$ for $y$.
$2y = 12 - 3x$. Divide both terms by 2.
Ready for more? Take the Unit 2 test.