1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Warm Up
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

3. 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

4. Sunshine State Standards
MA.6.A.3.3 Works backward with two-step functions rules to undo expressions.
Also MA.6.A.3.2

5. Additional Example 1A: 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

6. Additional Example 1A Continued
Check
18 + 3x = 30
Substitute 4 for x in the
equation.
18 + 3(4) ? = 30 ? = ? =
4 is the solution.

7. 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

8. Additional Example 1B: 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

9. Additional Example 1B Continued
Check x 3
– 2 = 1 9 3
Substitute 9 for x in the
equation. ? = – ? =
3 – ? =
9 is the solution.

10. Additional Example 1C: Solving Two-Step Equations
Solve. Check the answer.
x + 19 4
= 6
x + 19 4
Multiply both sides by 4 to
undo the division.
4 · = 4 · 6
x + 19
= 24
Subtract both sides by 19 to
undo the addition.
– – 19
x = 5

11. Additional Example 1C Continued
Check
x + 19 4
= 6
Substitute 5 for x in the
equation.
5 + 19 4
= 6 24 4 6 ? = ? =
5 is the solution.

12. Check It Out: Example 1A
Solve each equation .
7 x – 5 = 23
x = 4 7x 7
7 x 28 =

13. Check It Out: Example 1B
Solve each equation .
x – 16 = 9 3
x – 16 = 9
x = 75 x 3 25 =
3 ·
3 · 25

14. Check It Out: Example 1C
Solve. Check the answer.
x - 9 10
= 49
10 · =10 · 49
=490
x - 9 10 x
499 =

15. Additional Example 2: 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. Additional Example 2 Continued
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 2
Kaia earned $425 last week. She wants to put $350 in the bank and buy some DVDs. Each DVD costs $25. Write a two-step equation to represent the situation. Then solve the equation. How many DVDs can she buy?
Let x represent the number of DVDs purchased.
25x = 425
= - 350
25x 75

18. Check It Out: Example 2 Continued75 = 25 25
x = 3 Kaia can buy 3 DVDs.

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. The function rule is x – 8 = y 2 – 8 = 3
Check It Out: Example 3
The rule for a certain function is to multiply the input by 2 and subtract 8. Find the input value when the output is 3.
The function rule is x – 8 = y 2 x 2
– 8 = 3 x 2 = 11 x 2 2 =

23. Check It Out: 3 Continued
x = 22
The input value is 22.