1. Marvelous Monday Let’s demonstrate “ON TASK” behavior Find Seat
Sharpen pencil (if necessary)
Open notebook write today’s date
Write the following problems below and simplify
2x – 4x + 3(6x2 – 6) + 10
½(6x – 10) + ¼ (24x + 12)
8x2 + 3x – 2 + 6x2 – 10 – 7x

2. Solving
2-step and multi-step
Equations

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

4. Steps for Solving Two-Step Equations
Solve for any Addition or Subtraction on the variable side of equation by “undoing” the operation from both sides of the equation.
Solve any Multiplication or Division from variable side of equation by “undoing” the operation from both sides of the equation.

5. Opposite Operations
Addition 
Subtraction
Multiplication 
Division

6. Helpful Hints?
Identify what operations are on the variable side. (Add, Sub, Mult, Div)
“Undo” the operation by using inverse operation.
Whatever you do to one side, you must do to the other side to keep equation balanced.

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

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

9. Examples of more one-step equations

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

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

12. 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.

13. Solving 2 Step Equations
REMEMBER

14. 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.

15. 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

16. 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

17. 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.

18. 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.

19. 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

20. 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

21. 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

22. 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

23. Solving 2 Step Equations

24. Solving 2 Step Equations

25. 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.

26. #11
Review
1) Undo the addition or subtraction operation first, by using inverse operations.
2) Undo the multiplication or division second, by using inverse operations.

27. Homework!