1. Objectives Solve a formula for a given variable.
Solve an equation in two or more variables for one of the variables.

2. Solving for a Variable
Step 1 Locate the variable you are asked to solve for in the equation.
Step 2 Identify the operations on this variable and the order in which they are applied.
Step 3 Use inverse operations to undo operations and isolate the variable.

3. Example 1: Application
The formula C = d gives the circumference of a circle C in terms of diameter d. The circumference of a bowl is 18 inches. What is the bowl's diameter? Leave the symbol  in your answer.

4. Check It Out! Example 1
Solve the formula d = rt for t. Find the time in hours that it would take Ernst Van Dyk to travel 26.2 miles if his average speed was 18 miles per hour.
d = rt
Now use this formula and the information given in the problem.

5. Check It Out! Example 1
Solve the formula d = rt for t. Find the time in hours that it would take Ernst Van Dyk to travel 26.2 miles if his average speed was 18 miles per hour.
Van Dyk’s time was about 1.46 hours.

6. Example 2A: Solving Formulas for a Variable
The formula for the area of a triangle is A = bh,
where b is the length of the base, and is the height. Solve for h.
A = bh
2A = bh

7. Example 2B: Solving Formulas for a Variable
The formula for a person’s typing speed is
,where s is speed in words per minute,
w is number of words typed, e is number of errors, and m is number of minutes typing. Solve for e.

8. Check It Out! Example 2
The formula for an object’s final velocity is f = i – gt, where i is the object’s initial velocity, g is acceleration due to gravity, and t is time. Solve for i.
f = i – gt

9. A formula is a type of literal equation
A formula is a type of literal equation. A literal equation is an equation with two or more variables. To solve for one of the variables, use inverse operations.

10. Example 3: Solving Literal Equations
A. Solve x + y = 15 for x.
B. Solve pq = x for q.

11. Lesson Quiz: Part 1
Solve for the indicated variable. 1. 2.
3. 2x + 7y = 14 for y 4.
for h
P = R – C for C
C = R – P
for m
m = x(k – 6 ) 5.
for C
C = Rt + S

12. Lesson Quiz: Part 2
Euler’s formula, V – E + F = 2, relates the number of vertices V, the number of edges E, and the number of faces F of a polyhedron.
6. Solve Euler’s formula for F.
F = 2 – V + E
7. How many faces does a polyhedron with 8 vertices and 12 edges have? 6