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Transparency 4

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3. Solve two-step equations
Objective
Solve two-step equations
Example 4-4b

4. An equation that has two different operations
Vocabulary
Two-step equation
An equation that has two different operations
Example 4-4b

5. Example 1 Solve a Two-Step Equation
Example 4 Use an Equation to Solve a Problem
Lesson 4 Contents

6. Ask “what is being done to the variable first?”
Write the equation.
Solve
Ask “what is being done to the variable first?”
4x is being added by 3
4x = 19
4x = 4x
4x + 3
Do the inverse operation on each side
Bring down 4x + 3
Subtract 3
Bring down = 19
Subtract 3
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Example 4-1a

7. Use the Identify Property to add 4x + 0
Bring down 4x
Solve
Combine “like” terms
Bring down =
4x =
Combine “like” terms 4x
4x + 0 =
4x + 0 = 16
4x + 0
Use the Identify Property to add 4x + 0
4x = 16
Ask “what is being done to the variable?”
x is being multiplied by 4
Do the inverse operation on each side
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Example 4-1a

8. Using the fraction bar, divide 4x by 4
Bring down 4x = 16
Solve
Using the fraction bar, divide 4x by 4
4x =
Divide 16 by 4
4x + 0 = 16
Combine “like” terms
4x = 16
Bring down  x =
4x = 16
Combine “like” terms 4 4
Use the Identify Property to multiply 1  x
1  x = 4 1
1  x =
x = 4
Answer: x = 4
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Example 4-1a

9. Solve
Answer: t = 7
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Example 4-1b

10. Ask “what is being done to the variable first?”
Write the equation.
Solve
Ask “what is being done to the variable first?”
-3c is being added by 9
-3c = 3
-3c = 3 - 9
-3c + 9
-3c
Do the inverse operation on each side
Bring down -3c + 9
Subtract 9
Bring down = 3
Subtract 9
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Example 4-2a

11. Use the Identify Property to add -3c + 0 -3c -3c + 0 = -6 -3c + 0 =
Bring down -3c
Combine “like” terms
Solve
Bring down =
-3c = 3 - 9
Combine “like” terms
Use the Identify Property to add -3c + 0
-3c
-3c + 0 = -6
-3c + 0 =
-3c + 0
-3c = -6
Ask “what is being done to the variable?”
c is being multiplied by -3
Do the inverse operation on each side
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Example 4-2a

12. Using the fraction bar, divide -3c by -3
Bring down -3c = -6
Solve
Using the fraction bar, divide -3c by -3
Divide -6 by -3
-3c = 3 - 9
Combine “like” terms
-3c + 0 = -6
-3c + 0 =
-3c + 0
-3c
Bring down  c =
-3c = -6
Combine “like” terms
-3c = -6
Use the Identify Property to multiply 1  c -3 -3 1
1  c = 2
1  c =
c = 2
Answer: c = 2
2/4
Example 4-2a

13. Solve
Answer: k = -3
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Example 4-2b

14. Ask “what is being done to the variable first?”
Write the equation.
Solve
Ask “what is being done to the variable first?”
3t is being added by 6
t = 0
t = 0 - 6 6
6 - 6
Do the inverse operation on each side
Bring down 6
Subtract 6
Bring down + 3t = 0
Subtract 6
3/4
Example 4-3a

15. Use the Identify Property to add 0 + 3t
Combine “like” terms
Bring down +3t =
Solve
Combine “like” terms
t = 0 - 6
Use the Identify Property to add 0 + 3t
0 + 3t = - 6
0 + 3t =
Ask “what is being done to the variable?”
3t = - 6
t is being multiplied by 3
Do the inverse operation on each side
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Example 4-3a

16. Do the inverse operation on each side
Solve
Bring down 3t = -6
Using the fraction bar, divide 3t by 3
t = 0 - 6
Divide -6 by 3
0 + 3t = - 6
0 + 3t =
Combine “like” terms
3t = - 6
Bring down  t =
3t = - 6
Combine “like” terms 3 3
Use the Identify Property to multiply 1  t
1 t = -2 1
1 t =
t = -2
Answer: t = -2
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Example 4-3a

17. Solve
Answer: 8 = x
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Example 4-3b

18. 76,000 Georgia. three times the number
There are 76,000 acres of state parkland in Georgia. This is 4,000 acres more than three times the number of acres of state parkland in Mississippi. How many acres of state parkland are there in Mississippi?
4,000 acres more than
three times the number
76,000 =
76,000 = 3x + 4,000
76,000
Georgia has 76,000 acres
“this is” refers to =
Refers to + 4,000
Refers to 3x
Solve the 2-step equation
4/4
Example 4-4a

19. 76,000 Georgia. three times the number
There are 76,000 acres of state parkland in Georgia. This is 4,000 acres more than three times the number of acres of state parkland in Mississippi. How many acres of state parkland are there in Mississippi?
4,000 acres more than
three times the number
Ask “what is being done to the variable first?”
76,000 = 3x + 4,000
76,
76, = 3x + 4,000
76,000
76, = 3x + 4, ,000
3x is being added by 4,000
Do the inverse operation on each side
Bring down 76,000
Subtract 4,000
Bring down = 3x + 4,000
Subtract 4,000
4/4
Example 4-4a

20. 76,000 Georgia. three times the number
There are 76,000 acres of state parkland in Georgia. This is 4,000 acres more than three times the number of acres of state parkland in Mississippi. How many acres of state parkland are there in Mississippi?
4,000 acres more than
three times the number
Combine “like” terms
76,000 = 3x + 4,000
76, = 3x + 4, ,000
72,000 = 3x
72,000 = 3x + 0
72,000
Bring down =3x
72,000 = 3x
Combine “like” terms
Use the Identify Property to add 3x + 0
4/4
Example 4-4a

21. 76,000 Georgia. three times the number
There are 76,000 acres of state parkland in Georgia. This is 4,000 acres more than three times the number of acres of state parkland in Mississippi. How many acres of state parkland are there in Mississippi?
4,000 acres more than
three times the number
Ask “what is being done to the variable?”
76,000 = 3x + 4,000
76, = 3x + 4, ,000
72,000 = 3x
72,000
72,000 = 3x + 0
x is being multiplied by 3
72,000 = 3x
Do the inverse operation on each side
72,000 = 3x
Bring down 72,000 = 3x 3
Using the fraction bar, divide 72,000 by 3
4/4
Example 4-4a

22. 76,000 Georgia. three times the number
There are 76,000 acres of state parkland in Georgia. This is 4,000 acres more than three times the number of acres of state parkland in Mississippi. How many acres of state parkland are there in Mississippi?
4,000 acres more than
three times the number
Divide 3x by 3
76,000 = 3x + 4,000
76, = 3x + 4, ,000
Combine “like” terms
72,000 = 3x + 0
72,000 = 3x
72,000
Bring down =
72,000 = 3x
Combine “like” terms
72,000 = 3x
Use the Identify Property to multiply 1  x 3 3
Answer: 24,000 acres = x
24,000 = 1  x
24,000
24,000 =
4/4
Example 4-4a

23. *
BASEBALL Matthew had 64 hits during last year’s baseball season. This was 8 less than twice the number of hits Gregory had. How many hits did Gregory have during last year’s baseball season?
Answer: x = 36 hits
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Example 4-4b

24. Solving Two-Step Equations
Assignment
Lesson 4:4
Solving Two-Step Equations
All
End of Lesson 4