1. Solving Equations as Formulas
Algebra 1 ~ Chapter 3.8
Solving Equations as Formulas

2. Solving Formulas Some equations contain more than one variable.
y = mx+b, P = a+b+c, A = ½bh
At times, you will need to solve these equations for one of the variables.
If the question asked you to solve for x, that would mean to get x by itself on one side of the equation, with no x’s on the other side. (x = __ )
Solve just like you did with equations that only had one variable (undo add/sub then mult/div)

3. How to Solve Formulas
Example - Solve the equation A = ½bh, for h.
Ask yourself:
What is being done to h, the variable being solved for? (This is the same process as when we drove the car, and then we turned it around to go back home…)
How do I undo what is being done?
So: Just treat all other variables as if they were numbers, and repeat what we’ve already been doing.

4. A = ½bh, solve for h 2A = (½bh)2 2A = bh b b h =
Solve for h means getting h = _________
Get rid of ½ by multiplying both sides by 2.
Get h alone by “undoing” bh. Divide each side by b.

5. Example 1 t t Get r = ________ Solve d = r∙t, for r
Undo multiplication
Solve d = r∙t, for r
d = r ∙ t
t t

6. Example 2 Solve P = 2L + 2W, for L P – 2W = 2L 2 2 -2W -2W
Get “L” by itself, L=_______
Want to get rid of the whole term 2w, so subtract 2w from both sides of the equation.
Undo 2L by dividing both sides by 2.

7. Example 3 Want to get x = __ “Undo” subtraction “Undo” multiplication
Solve ax – c = b for x.
+c +c
ax = b + c
a a
Want to get x = __
“Undo” subtraction
“Undo” multiplication

8. Example 4 Want to get y = __ Undo addition Undo multiplication
Solve 6x – 3y = 12 for y.
-6x x
-3y = -6x + 12
y = 2x – 4
Want to get y = __
Undo addition
Undo multiplication

9. Solve A = ½bh for b Solve 12x + 4y = 16 for y Solve V = lwh for h
Lesson Quiz
Solve A = ½bh for b
Solve 12x + 4y = 16 for y
Solve V = lwh for h