1. Solving Two-Step Equations
10-1
Solving Two-Step Equations
Course 3
Warm Up
Problem of the Day
Lesson Presentation

2. Solving Two-Step Equations
Course 3
10-1
Solving Two-Step Equations
Warm Up
Solve.
1. x + 12 = 35
2. 8x = 120
= 7
4. –34 = y + 56
x = 23
x = 15 y9
y = 63
y = –90

3. Solving Two-Step Equations
Course 3
10-1
Solving Two-Step Equations
Problem of the Day
x is an odd integer. If you triple x and then subtract 7, you get a prime number. What is x? (Hint: Think about what the prime number must be in order for x to be an odd.)
x = 3

4. Solving Two-Step Equations
Course 3
10-1
Solving Two-Step Equations
Learn to solve two-step equations.

5. Solving Two-Step Equations
Course 3
10-1
Solving Two-Step Equations
Sometimes more than one inverse operation is needed to solve an equation. Before solving, ask yourself, “What is being done to the variable, and in what order?” Then work backward to undo the operations.

6. Additional Example 1: Problem Solving Application
Course 3
10-1
Solving Two-Step Equations
Additional Example 1: Problem Solving Application
The mechanic’s bill to repair Mr. Wong’s car was $650. The mechanic charges $45 an hour for labor, and the parts that were used cost $443. How many hours did the mechanic work on the car?

7. Understand the Problem
Course 3
10-1
Solving Two-Step Equations
Additional Example 1 Continued 1
Understand the Problem
List the important information:
The answer is the number of hours the mechanic worked on the car.
The parts cost $443.
The labor cost $45 per hour.
The total bill was $650.
Let h represent the hours the mechanic worked.
Total bill = Parts + Labor
= h

8. Additional Example 1 Continued
Course 3
10-1
Solving Two-Step Equations
Additional Example 1 Continued 2
Make a Plan
Think: First the variable is multiplied by 45, and then 443 is added to the result. Work backward to solve the equation. Undo the operations in reverse order: First subtract 443 from both sides of the equation, and then divide both sides of the new equation by 45.

9. Additional Example 1 Continued
Course 3
10-1
Solving Two-Step Equations
Additional Example 1 Continued
Solve 3
650 = h
–443 –443 Subtract to undo the addition.
207 = h h =
Divide to undo multiplication.
4.6 = h
The mechanic worked for 4.6 hours on Mr. Wong’s car.

10. Additional Example 1 Continued
Course 3
10-1
Solving Two-Step Equations
Additional Example 1 Continued
Look Back 4
If the mechanic worked 4.6 hours, the labor would be $45(4.6) = $207. The sum of the parts and the labor would be $443 + $207 = $650.

11. Solving Two-Step Equations
Course 3
10-1
Solving Two-Step Equations
Try This: Example 1
The mechanic’s bill to repair your car was $850. The mechanic charges $35 an hour for labor, and the parts that were used cost $275. How many hours did the mechanic work on your car?

12. Understand the Problem
Course 3
10-1
Solving Two-Step Equations
Try This: Example 1 Continued 1
Understand the Problem
List the important information:
The answer is the number of hours the mechanic worked on your car.
The parts cost $275.
The labor cost $35 per hour.
The total bill was $850.
Let h represent the hours the mechanic worked.
Total bill = Parts + Labor
850 = h

13. Try This: Example 1 Continued
Course 3
10-1
Solving Two-Step Equations
Try This: Example 1 Continued 2
Make a Plan
Think: First the variable is multiplied by 35, and then 275 is added to the result. Work backward to solve the equation. Undo the operations in reverse order: First subtract 275 from both sides of the equation, and then divide both sides of the new equation by 35.

14. Try This: Example 1 Continued
Course 3
10-1
Solving Two-Step Equations
Try This: Example 1 Continued
Solve 3
850 = h
–275 –275 Subtract to undo the addition.
575 = h h =
Divide to undo multiplication.
16.4  h
The mechanic worked for about 16.4 hours on your car.

15. Try This: Example 1 Continued
Course 3
10-1
Solving Two-Step Equations
Try This: Example 1 Continued
Look Back 4
If the mechanic worked 16.4 hours, the labor would be $35(16.4) = $574. The sum of the parts and the labor would be $275 + $574 = $849.

16. Additional Example 2A: Solving Two-Step Equations
Course 3
10-1
Solving Two-Step Equations
Additional Example 2A: Solving Two-Step Equations
Solve. n3
A = 22
Think: First the variable is divided by 3, and then 7 is added. To isolate the variable, subtract 7, and then multiply by 3.
+ 7 = 22 n3
– 7 – Subtract to undo addition. n3
= 15
Multiply to undo division.
3  = 3  15 n3
n = 45

17. Additional Example 2A Continued
Course 3
10-1
Solving Two-Step Equations
Additional Example 2A Continued
+ 7 = 22 n3
Check ?
+ 7 = 22
Substitute 45 into the original equation.
= 22 ? 

18. Additional Example 2B: Solving Two-Step Equations
Course 3
10-1
Solving Two-Step Equations
Additional Example 2B: Solving Two-Step Equations
B. 2.7 = –1.3m + 6.6
Think: First the variable is multiplied by –1.3, and then 6.6 is added. To isolate the variable, subtract 6.6, and then divide by –1.3.
2.7 = –1.3m + 6.6
– –6.6
Subtract to undo addition.
–3.9 = –1.3m
– –1.3
–3.9 = –1.3m
Divide to undo multiplication.
3 = m

19. Additional Example 2C: Solving Two-Step Equations
Course 3
10-1
Solving Two-Step Equations
Additional Example 2C: Solving Two-Step Equations
C = 9
y – 4 3
Think: First 4 is subtracted from the variable, and then the result is divided by 3. To isolate the variable, multiply by 3, and then add 4.
= 9
y – 4 3
3 · · Multiply to undo division. =
y – 4 3
y – 4 = 27
Add to undo subtraction.
y = 31

20. Solving Two-Step Equations
Course 3
10-1
Solving Two-Step Equations
Try This: Example 2A
Solve. n4
A = 29
Think: First the variable is divided by 4, and then 5 is added. To isolate the variable, subtract 5, and then multiply by 4.
+ 5 = 29 n4
– 5 – Subtract to undo addition.
Multiply to undo division.
4  = 4  24 n4
n = 96

21. Try This: Example 2A Continued
Course 3
10-1
Solving Two-Step Equations
Try This: Example 2A Continued
+ 5 = 29 n4
Check ?
+ 5 = 29
Substitute 96 into the original equation.
= 29 ? 

22. Solving Two-Step Equations
Course 3
10-1
Solving Two-Step Equations
Try This: Example 2B
B. 4.8 = –2.3m + 0.2
Think: First the variable is multiplied by –2.3, and then 0.2 is added. To isolate the variable, subtract 0.2, and then divide by –2.3.
4.8 = –2.3m + 0.2
– –0.2
Subtract to undo addition.
4.6 = –2.3m
– –2.3
4.6 = –2.3m
Divide to undo multiplication.
–2 = m

23. Solving Two-Step Equations
Course 3
10-1
Solving Two-Step Equations
Try This: Example 2C
C = 8
y – 2 4
Think: First 2 is subtracted from the variable, and then the result is divided by 4. To isolate the variable, multiply by 4, and then add 2.
= 8
y – 2 4
4 · · Multiply to undo division. =
y – 2 4
y – 2 = 32
Add to undo subtraction.
y = 34

24. Solving Two-Step Equations Insert Lesson Title Here
Course 3
10-1
Solving Two-Step Equations
Insert Lesson Title Here
Lesson Quiz
Solve.
– 3 = 10
2. 7y + 25 = –24
3. –8.3 = –3.5x
= 3
5. The cost for a new cell phone plan is $39 per month plus a one-time start-up fee of $78. If you are charged $1014, how many months will the contract last? x –9
x = –117
y = –7
x = 6.2 y
y = 28
24 months