1. Solving Two Step Equations 11-1
Notes 13
Solving Two Step Equations
11-1

2. When you solve equations that have one
operation, you use an inverse operation to
isolate the variable.
n + 7 = 15
– –7
n = 8
You can also use inverse
operations to solve equations that have more
than one operation.
2x + 3 = 23
You need to use
another operation
to isolate x.
– 3 – 3
2x = 20

3. Additional Example 1A: Solving Two-Step Equations Using Division
Solve. Check each answer.
9c + 3 = 39
9c + 3 = 39
– 3 –3
Subtract 3 from both sides.
9c = 36 9c 9
= 36
Divide both sides by 9.
c = 4

4. Additional Example 1A Continued
Check.
9c + 3 = 39
9(4) + 3 ? = 39
Substitute 4 for c. ? = ? =
4 is a solution.

5. Reverse the order of operations when solving equations that have more than one operation.
Helpful Hint

6. Additional Example 1B: Solving Two-Step Equations Using Division
Solve. Check the answer.
–34 = –4m – 6
–34 = –4m – 6
Add 6 to both sides.
–28 = –4m
–28 –4
= –4m
Divide both sides by –4.
7 = m

7. Additional Example 1B Continued
Check.
–4m – 6 = –34
–4(7) – 6 ? =
–34
Substitute 7 for m.
–28 – 6 –34 ? = ? =
–34 –34
7 is a solution.

8. Check It Out: Example 1A
On your own.
Solve. Check the answer.
7c + 6 = 48

9. Check It Out: Example 1B
On your own.
Solve. Check the answer.
–6m – 8 = –50

10. Additional Example 2A: Solving Two-Step Equations Using Multiplication
Solve. y 5
6 +
= 21 y 5
6 +
= 21
– –6
Subtract 6 from both sides. y 5
= 15
(5)‏ y 5
= (5)15
Multiply both sides by 5.
y = 75

11. Additional Example 2B: Solving Two-Step Equations Using Multiplication
Solve. x 7
– 11 = 9 x 7
– 11 = 9
Add 11 to both sides. x 7
= 20 x 7
(7)‏
= (7)20
Multiply both sides by 7.
x = 140

12. Check It Out: Example 2A
Solve. y 2
8 +
= 48

13. Check It Out: Example 2B
Solve. x 5
– 31 = 19

14. Additional Example 3: Consumer Math Application
Jamie rented a canoe while she was on vacation. She paid a flat rental fee of $85.00, plus $7.50 each day. Her total cost was $ For how many days did she rent the canoe?
Let d represent the number of days she rented the canoe.
7.5d + 85 = 130
– –85
Subtract 85 from both sides.
7.5d = 45
7.5d = 45
Divide both sides by 7.5.
7.5
7.5
d = 6
Jamie rented the canoe for 6 days.