1. Problem of the Day
Janet used a pedometer to count her steps. The first day and third day she took exactly the same number of steps. The second day she took 1,739 steps. If she took 6,125 steps in all those 3 days, how many steps did she take the first day?
2,193 steps

2. Solving Two-Step Equations

3. Solving Two-Step Equations
MA.6.A.3.3 Works backward with two-step functions rules to undo expressions.
Also MA.6.A.3.2

4. Solving Two-Step Equations
Essential Question:
How are equations applied in the real world?

5. Warm Up – Refresh your memory:
Solve each equation.
1. 15x = 225
2. y + 2 = 10
Find the value of each expression.
3. 18 – 6 3  5
 (16  4) – 2
x = 15
y = 8 8 17

6. Solving Two-Step Equations
Solve each equation.
18 + 3x = 30
18 + 3x = 30
– –18
Subtract 18 from both sides to
undo the addition.
3x = 12 3x 3
= 12
Divide both sides by 3 to undo
the multiplication.
x = 4

7. Check 18 + 3x = 30 Substitute 4 for x in the equation. 18 + 3(4) 30? = 30 ? = ? =
4 is the solution.

8. Undo operations in the reverse of the Order of Operations
Undo operations in the reverse of the Order of Operations. First undo addition or subtraction. Then undo multiplication or division.
Helpful Hint

9. Solving Two-Step Equations
Solve. Check the answer. x 3
– 2 = 1 x 3
– 2 = 1
Add 2 to both sides to undo
the subtraction. x 3
= 3
3 · = 3 · 3 x 3
Multiply both sides by 3.
x = 9

10. Check x 3 – 2 = 1 9 3 Substitute 9 for x in the equation. – 2 1
– 2 = 1 9 3
Substitute 9 for x in the
equation. ? = – ? =
3 – ? =
9 is the solution.

11. Check It Out: Example 1A
Solve each equation.
12 + 3x = 27
12 + 3x = 27
– –12
Subtract 12 from both sides to
undo the addition.
3x = 15 3x 3
= 15
Divide both sides by 3 to undo
the multiplication.
x = 5

12. Check It Out: Example 1A Continued
Substitute 5 for x in the
equation.
12 + 3(5) ? = 27 ? = ? =
5 is the solution.

13. Check It Out: Example 1B
Solve. Check the answer. x 2
– 1 = 2 x 2
– 1 = 2
Add 1 to both sides to undo
the subtraction. x 2
= 3
2 · = 2 · 3 x 2
Multiply both sides by 2.
x = 6

14. Check It Out: Example 1B Continued2
– 1 = 2 6 2
Substitute 6 for x in the
equation. ? = – ? =
3 – ? =
6 is the solution.

15. Consumer Math Application
Nancy saved $87 of the money she made babysitting. She wants to buy CDs that cost $15 each, along with a set of headphones that costs $12. How many CDs can she buy?
Write a two-step equation to represent the situation.
Let x represent the number of CDs Nancy can buy.
cost of a CD times
the number of CDs
cost of
headphones
total cost + =
15x + 12 = 87
The equation 15x + 12 = 87 represents the situation.

16. Nancy saved $87 of the money she made babysitting
Nancy saved $87 of the money she made babysitting. She wants to buy CDs that cost $15 each, along with a set of headphones that costs $12. How many CDs can she buy?
Solve the equation.
15x = 87
– –12
Subtract 12 from both sides.
15x = 75
15x = 75
Divide both sides by 15. 15 15
x = 5
Nancy can buy 5 CDs.

17. Check It Out: Example 2B
Jack rented a car while they were on vacation. He paid a rental fee of $20.00 per day, plus 20¢ a mile. He paid $25.00 for mileage and his total bill for renting the car was $ For how many days did he rent the car?
Write a two-step equation to represent the situation.
Let d represent the number of days he rented the car.
cost of rental fee
times number of days
cost of
mileage
total cost + =
20d + 25 =
165
The equation 20d + 25 = 165 represents the situation.

18. Check It Out: Example 2B
Jack rented a car while they were on vacation. He paid a rental fee of $20.00 per day, plus 20¢ a mile. He paid $25.00 for mileage and his total bill for renting the car was $ For how many days did he rent the car?
Solve the equation.
20d + 25 = 165
– – 25
Subtract 25 from both sides.
20d = 140
20d = 140
Divide both sides by 20. 20 20
d = 7
Jack rented the car for 7 days.

19. Additional Example 3: Working Backward with Function Rules
The rule for a certain function is to multiply the input by 5 and subtract 4. Find the input value when the output is 11.
The function rule is 5
times
input
minus 4
equals
output 5 x x – 4 = y

20. Additional Example 3 Continued
The rule for a certain function is to multiply the input by 5 and subtract 4. Find the input value when the output is 11.
Use the function rule and the given
output value to write an equation.
5x – 4 = 11
Add 4 to both sides to undo the
subtraction.
5x = 15
5x = 15
Divide both sides by 5. 5 5
x = 3
The input value is 3.

21. Additional Example 3 Continued
The rule for a certain function is to multiply the input by 5 and subtract 4. Find the input value when the output is 11.
Check Substitute the input value into the rule.
5(3) – 4 = 15 – 4 = 11
check

22. Check it Out: Example 3
The rule for a certain function is to multiply the input by 6 and subtract 3. Find the input value when the output is 9.
The function rule is 6
times
input
minus 3
equals
output 6 x x – 3 = y

23. Check it Out Example 3 Continued
The rule for a certain function is to multiply the input by 6 and subtract 3. Find the input value when the output is 9.
Use the function rule and the given
output value to write an equation.
6x – 3 = 9
Add 3 to both sides to undo the
subtraction.
6x = 12
6x = 12
Divide both sides by 6. 6 6
x = 2
The input value is 2.

24. Check it Out Example 3 Continued
The rule for a certain function is to multiply the input by 6 and subtract 3. Find the input value when the output is 9.
Check Substitute the input value into the rule.
6(2) – 3 = 12 – 3 = 9
check

25. Lesson Quiz for Student Response Systems
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems 25 25

26. Solve each equation. Check your answer. 1. – 7 = 1 2. 22x + 11 = 143
Lesson Quiz
Solve each equation. Check your answer.
– 7 = 1
2. 22x + 11 = 143 3. 4. x 12
x = 96
x = 6
x + 9 5
= 7
x = 26
9x – 6 = 39
x = 5
5. In two days, Yasmine drove 505 miles to visit her
cousin. The first day, she drove 230 miles. The next
day Yasmine drove 5 hours at a constant speed. How
fast did Yasmine drive on the second day?
55 mi/h

27. Lesson Quiz for Student Response Systems
1. Solve 4x + 3 = 27.
A. x = 6
B. x = 7.5
B. x = 8
B. x = 96 27 27

28. Lesson Quiz for Student Response Systems
3. Solve
A. x = 15
B. x = 20
C. x = 60
D. x = 100 28 28