1. One and Two Step Equations and Inequalties

2. Inverse Operations 5 + 12 = 17 -12 = -12 5 = 5
These are operations that undo each other.
For Example:
I get back to 5 by subtracting what I added.
= 17
-12 = -12
5 = 5

3. Inverse Operations What is the opposite/inverse of multiplication?
What is the opposite/inverse of addition?
What is the opposite/inverse of subtraction?
What is the opposite/inverse of division?
Division
Subtraction
Addition
Multiplication

4. Isolating the Variable
- When you get the variable all by itself.
X = -3

5. Type 1: -3x + 10 = 1 - 10 -10 -3x + 0 = -9 -3 -3 x = 3
You need to get x all by itself!
-3x + 10 = 1
Get rid of the adding or subtracting FIRST!
- 10
-10
Do the Opposite!
-3x
+ 0 = -9
Now get rid of the multiplication or division! -3 -3
Do the Opposite! x = 3

6. You try: -2x + 12 = 2 - 12 -12 -2x + 0 = -10 -2 -2 x = 5
Get rid of the adding or subtracting FIRST!
- 12
-12
Do the Opposite!
-2x
+ 0 =
-10
Now get rid of the multiplication or division! -2 -2
Do the Opposite! x = 5

7. Type 2:
You need to get y all by itself! y 2
- 4 = 12
Get rid of the adding or subtracting FIRST! +4 +4
Do the Opposite! y 2
Now get rid of the multiplication or division! 2● +0 = 16 ●2
Do the Opposite! y = 32

8. You Try: y 3
- 5 = 4
Get rid of the adding or subtracting FIRST! +5 +5
Do the Opposite! y 3
Now get rid of the multiplication or division! 3● +0 = 9 ●3
Do the Opposite! y = 27

9. Type 3: 2 5 - - x = -4 2 5 -5● x = -4 ●-5 - 2x = 20 2 2 x = 10
Bring the negative up or down 2 5 - - x
= -4 2 5
Now get rid of the division!
-5● x
= -4
●-5
Do the Opposite! - 2x = 20
Now get rid of the multiplication! 2 2
Do the Opposite! x = 10

10. You Try: 3 7 - - x = -3 3 7 -7● x = -3 ●-7 - 3x = 21 3 3 x = 7
Bring the negative up or down 3 7 - - x
= -3 3 7
Now get rid of the division!
-7● x
= -3
●-7
Do the Opposite! - 3x = 21
Now get rid of the multiplication! 3 3
Do the Opposite! x = 7

11. Type 1:
You need to get a all by itself!
Get rid of the adding or subtracting FIRST!
5 – a = 6
- 5 -5
Do the Opposite! -a = 1
Now get rid of the NEGATIVE SIGN! -1 -1
Divide by -1 a = -1

12. You Try: -3 – x = 15 +3 +3 -x = 18 -1 -1 x = -18
You need to get x all by itself!
Get rid of the adding or subtracting FIRST!
-3 – x = 15 +3 +3
Do the Opposite! -x = 18
Now get rid of the NEGATIVE SIGN! -1 -1
Divide by -1 x =
-18

13. Type 2: -x – 12 = 15 +12 +12 -x +0 = 27 -1 -1 x = -27
You need to get x all by itself!
-x – 12 = 15
Get rid of the adding or subtracting FIRST!
+12
+12
Do the Opposite!
Now get rid of the NEGATIVE SIGN! -x +0 = 27
Divide by -1 -1 -1 x =
-27

14. You Try: -x + 8 = -1 -8 -8 -x +0 = -9 -1 -1 x = 9
You need to get x all by itself!
-x + 8 = -1
Get rid of the adding or subtracting FIRST! -8 -8
Do the Opposite!
Now get rid of the NEGATIVE SIGN! -x +0 = -9
Divide by -1 -1 -1 x = 9

15. Type 3:
You need to get x all by itself!
Get rid of the adding or subtracting FIRST!
8 + 2x = -2
- 8 -8
Do the Opposite! 2x =
-10
Now get rid of the Multiplication! 2 2
Do the Opposite x = -5

16. You Try: -3 - 6x = -21 +3 +3 -6x = -18 -6 -6 x = 3
You need to get x all by itself!
Get rid of the adding or subtracting FIRST!
-3 - 6x = -21 +3 +3
Do the Opposite!
-6x =
-18
Now get rid of the Multiplication! -6 -6
Do the Opposite x = 3

17. Solve & then graph the inequality.
Let's Try: 1 2 3 4 5 -1 -2 -3 -4 -5 -6 6

18. Solve & then graph the inequality.
You Try: 1 2 3 4 5 -1 -2 -3 -4 -5 -6 6

19. Solve & then graph the inequality.
Let's Try: 1 2 3 4 5 -1 -2 -3 -4 -5 -6 6

20. Solve & then graph the inequality.
You Try: 1 2 3 4 5 -1 -2 -3 -4 -5 -6 6

21. Solve & then graph the inequality.
Let's Try:
When multiplying or dividing by a negative you must FLIP the sign. 1 2 3 4 5 -1 -2 -3 -4 -5 -6 6

22. Solve & then graph the inequality.
You Try:
When multiplying or dividing by a negative you must FLIP the sign. 1 2 3 4 5 -1 -2 -3 -4 -5 -6 6

23. Solve & then graph the inequality.
You Try:
When multiplying or dividing by a negative you must FLIP the sign. 1 2 3 4 5 -1 -2 -3 -4 -5 -6 6