Holt Algebra 1

2-5 Solving for a Variable

Solve a formula for a given variable.

Solve an equation in two or more variables for one of the variables.

Objectives

Holt Algebra 1

2-5 Solving for a Variable

Solving for a VariableStep 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.

Holt Algebra 1

2-5 Solving for a Variable

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.

Holt Algebra 1

2-5 Solving for a Variable

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.

Now use this formula and the information given in the problem.

d = rt

Holt Algebra 1

2-5 Solving for a Variable

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.

Holt Algebra 1

2-5 Solving for a Variable

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

Holt Algebra 1

2-5 Solving for a Variable

Example 2B: Solving Formulas for a VariableThe 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.

Holt Algebra 1

2-5 Solving for a Variable

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

Holt Algebra 1

2-5 Solving for a Variable

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.

Holt Algebra 1

2-5 Solving for a Variable

Example 3: Solving Literal Equations

A. Solve x + y = 15 for x.

B. Solve pq = x for q.

Holt Algebra 1

2-5 Solving for a Variable

Lesson Quiz: Part 1

Solve for the indicated variable.

1.

2.

3. 2x + 7y = 14 for y

4.

P = R – C for C C = R – P

for m m = x(k – 6 )

5. for C C = Rt + S

for h

Holt Algebra 1

2-5 Solving for a Variable

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.

7. How many faces does a polyhedron with 8 vertices and 12 edges have?

F = 2 – V + E

6