1. Solving
2 Step
Equations

2. Solving 2 Step Equations
When you do something
to one side of an equation,

3. Solving 2 Step Equations
you have to do exactly
the same thing
to the other side.

4. Solving 2 Step Equations
To solve an equation means
to find every number that makes the equation true.

5. Solving 2 Step Equations
In the equation,
x is the number
you add to 7
to get 15.

6. Solving 2 Step Equations
What is the number?
8, of course.
So we would write the solution
x = 8

7. Solving 2 Step Equations
In some equations,
the solution is obvious.

8. Solving 2 Step Equations
But in other equations,
the solution is not so obvious.

9. Solving 2 Step Equations
Many times we need
a way to solve equations.
Especially if there is more
than one step to solve.

10. Solving 2 Step Equations
1) Undo the addition or subtraction operation first, by using inverse operations.
2) Undo the multiplication or division operation second, by using inverse operations.

11. Solving 2 Step Equations
REMEMBER

12. Solving 2 Step Equations
To solve any equation, you want to get the variable all by itself. You get the variable alone by using inverse operations.
Inverse Operations are like Opposites.

13. I am going to show you 2 ways to solve this equation.
Solving 2 Step Equations
I am going to show you 2 ways to solve this equation.
3x + 4 = 16
Hard way
Easy way
Undo Multiplication
or Division 1st
Undo Addition or Subtraction 1st

14. Solving 2 Step Equations
Hard way
Easy way
Undo Multiplication or Division 1st
Undo Addition or Subtraction 1st
3x + 4 = 16
3x + 4 = 16 3 3 3x 4 16 + =
3x = 12 3 3 3 3 3 4 16 x + = 3 3
x = 4 4 4 - - 3 3 12 x = 3 x = 4

15. Solving 2 Step Equations
1) GOAL:
Get the variable on one side
of the equation.
2) You always perform the same operation to
both sides of an equation.
3) To undo an operation you perform its opposite operation to both sides of the equation.
4) It is easier if you undo addition or subtraction before you undo multiplication or division.

16. Solving 2 Step Equations
2x + 4 = 10
Get the variable alone.
Subtract 4 from both sides.
2x = 6
__ __
+4 and -4 cancel out
Divide both sides by 2
x = 3
2 divided by 2 cancel to 1
2(3) +4 = 10
Show your check.
6 + 4 = 10
10 = 10
Finish your check.

17. Solving 2 Step Equations
3m - 10 = 17
Get the variable alone.
Add 10 to both sides.
3m = 27
__ __
+10 and -10 cancel out
Divide both sides by 3
m = 9
3 divided by 3 cancel to 1
3(9) – 10 = 17
Show your check.
27 – 10 = 17
Finish your check.
17 = 17

18. Solving 2 Step Equations
x 3
– 4 = 8
Get the variable alone.
Add 4 to both sides.
x 3
= 12
+ 4 and -4 cancel out.
x 3
Multiply both sides by 3.
3 ( ) = 3 12
3 divided by 3 cancel to 1
x = 36
Show your check. 36 3
– 4 = 8
Finish your check.
12 – 4 = 8
8 = 8

19. Solving 2 Step Equations
x 2
+ 6 = 14
Get the variable alone.
Subtract 6 from both sides.
x 2
= 8
+ 6 and -6 cancel out.
x 2
Multiply both sides by 2.
2 ( ) = 2 8
2 divided by 2 cancel to 1
x = 16 16 2
Show your check.
+ 6 = 14
8 + 6 = 14
Finish your check.
14 = 14

20. Solving 2 Step Equations
What Operation Do You Do?
FIRST SECOND
1) 3x + 8 = 24
Divide by 3
Subtract 8
2) 5x - 10 = 19
Divide by 5
Add 10
3) x = 20 2
Add 4
Multiply by 2
4) - 30 = -5x + 5
Divide by -5
Subtract 5

21. Solving 2 Step Equations

22. Solving 2 Step Equations

23. Solving 2 Step Equations
Think about what you need to do to isolate the variable.
Get rid of addition or subtraction first. Second get rid of multiplication or division.

24. Solving 2 Step Equations
The End!
Take out your study guide!

25. #11
Solve 2 Step Equations
1) Undo the addition or subtraction operation first, by using inverse operations.
2) Undo the multiplication or division second, by using inverse operations.

26. 2 Step Subtract/Multiply Equation
#12
3m - 10 = 17
Get the variable alone.
Add 10 to both sides.
__ __
3m = 27
+10 and -10 cancel out
Divide both sides by 3
m = 9
3 divided by 3 cancel to 1
3(9) – 10 =17
Show your check.
27 – 10 =17
Finish your check.
17 =17

27. 2 Step ADD/DIVIDE Equation
#13
2 Step ADD/DIVIDE Equation
x 2
+ 6 = 14
Get the variable alone.
Subtract 6 from both sides.
x 2
= 8
+ 6 and -6 cancel out.
x 2
Multiply both sides by 2.
( ) = 2 2
2 divided by 2 cancels out
x = 16 16 2
Show your check.
+ 6 = 14
8 + 6 = 14
Finish your check.
14 = 14

28. TEACHER NOTE: Use the following slides the next day when correcting homework.

29. HOMEWORK EXPLANATION

30. An Equation is like a balance scale
An Equation is like a balance scale. Everything must be equal on both sides. = 20
2x +5

31. What you do to one side of an equation, you must do to the other side to keep it balanced!= 20
2x +5 -5 -5

32. What you do to one side of an equation, you must do to the other side to keep it balanced!= 15 2x __ 2 __ 2

33. What you do to one side of an equation, you must do to the other side to keep it balanced!=
7.5 x

34. Try to solve this subtraction equation
How do you get n all by itself? = 18
n - 3 +3 +3

35. Try to solve this subtraction equation
How do you get n all by itself? = 21 n

36. Show your check by substituting your answer back into the original equation.= 18 21
n - 3

37. Try to solve this division equation
How do you get x all by itself? x 3 = •3 •3 15

38. Try to solve this division equation
How do you get x all by itself? x = 45

39. SHOW YOUR CHECK! 45 x 3 = 15

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