Solving Equations for a Variable A.K.A. Literal Equations Sometimes you have a formula, such as something from geometry, and you need to solve for some variable other than the "standard" one. For instance, the formula for the perimeter P of a square with sides of length s is P = 4s. You might need to solve this equation for s, so you can plug in a perimeter and figure out the side length. This process of solving a formula for a given variable is called "solving literal equations". One of the dictionary definitions of "literal" is "related to or being comprised of letters", and variables are sometimes referred to as literals. So "solving literal equations" seems to be another way of saying "taking an equation with lots of letters, and solving for one letter in particular." . Here's •
how "solving literal equations" works:
Solve
A = bh for b
I need to isolate b on one side of the equation and have everything else on the other side. Use inverse operations to do this. •
Solve
d = rt
r
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Solve
Q=
c+d for d 2
2Q = c + d 2Q – c = c + d – c 2Q – c = d Solve
P = 2l + 2w for w
PRACTICE
1. A = p + prt for r
2. A = p + prt for t
3. V = lwh for l
4. V = lwh for h
5. y = mx + b for b
6. y = mx + b for m
7. A = 2π r for π
8. V = π r 2 h for h
9. p =
100a for a t
1 11. A = bh for h 2
13. V =
3k for c t
10. y =
kx for x 2
12. R = 3b + 5ac for a
14. I × R 2 = P for I