1. Solving Inequalities

2. Vocabulary Review How would you say 5 > 2 ? What about x > 2 ?
Five is greater than 2.
What about x > 2 ?
x is greater than 2.
What could x be to make that statement true?
Come up with 5 possibilities.

3. Vocabulary Review How would you say 2 < 5 ?
Two is less than five.
How would you say x < 5 ?
x is less than 5.
What could x be to make that statement true?
Come up with 5 possibilities.

4. Vocabulary Review How would you say 5 ≥ x ? How would you say 2 ≤ x ?
Five is greater than or equal to x.
What could x be to make that statement true?
Come up with 5 possibilities.
How would you say 2 ≤ x ?
2 is less than or equal to x.

5. Graphing Practice

6. Let’s Graph! Graph x > 5 What are five possible values for x?
Are they shaded in on the graph?

7. Let’s Graph! Graph x ≥ 5 What are five possible values for x?
Are they shaded in on the graph?

8. Let’s Graph! Graph x < -3 What are five possible values for x?
Are they shaded in on the graph?

9. Let’s Graph! Graph x ≤ -3 What are five possible values for x?
Are they shaded in on the graph?

10. What rules can we make about graphing inequalities?
Possible Phrasing of Rules:
When dealing with < or >,
the circle will be empty.
When dealing with ≤ or ≥,
the circle will be filled in.
Shade in the direction of the answer,
< or ≤ goes towards
the left
> or ≥ goes towards
the right.

11. ADDING AND SUBTRACTING WITH INEQUALITIES

12. Is 5 > 2? YES. What would you get if you added 2 to each side?
7 > 4

13. Is 7 > 4? YES. What would you get if you added -5 to each side?
2 > -1

14. Is 2 > -1?
YES.
What would you get if you subtracted 7 from each side?
-5 > -8

15. Is -5 > -8?
YES.
What would you get if you subtracted -3 from each side?
-2 > -5

16. Is -2 > -5?
YES.
What rule can we make about adding or subtracting on each side of the inequality?

17. Possible Phrasing of Rule
If you add or subtract the same value on each side of an inequality sign, the sign
doesn’t change.

18. MULTIPLYING AND DIVIDING WITH INEQUALITIES

19. Is 5≤8? YES. What would you get if you multiplied each side by six?
30≤48

20. Is 30≤48?
YES.
What would you get if you divided each side by 2?
15≤24

21. Is 15≤24? YES. What would you get if you multiplied each side by -5?
-75≤-120

22. Is -75≤-120? NO. What would we have to do to make that statement true?
Flip the sign.

23. Is -75≥-120? YES. What would you get if you divided each side by -3?
25≥40

24. Is 25≥40? NO. What would we have to do to make that statement true?
Flip the sign.

25. Is 25≤40?
YES.
What rules can we make about multiplying and dividing on each side of an inequality?

26. POSSIBLE PHRASING OF RULE
If you multiply or divide each side by a positive number, the sign
stays the same.
If you multiply or divide each side by a negative number, the sign
flips.

27. Let’s Practice

28. Solve for x
x + 2 > 3 Subtract 2 from each side x > 1 Graph.

29. Solve for x
2x – 4 < 8 Add 4 to each side x < 12 Divide each side by 2 ÷2 ÷2 x < 6 Graph.

30. Solve for x
2x+3≥x-5 Subtract 3 from each side x≥x-8 Subtract x from each side. -x -x x≥-8 Graph.

31. Solve for x
2x≤x+2 Subtract x from each side. -x -x x≤2 Graph.

32. Solve for x
-8x-1≥15 Add 1 to each side x≥16 Divide each side by -8. ÷-8 ÷-8 x≤-2 Don’t forget to flip the sign! Graph.

33. Solve for x
𝑥 −2 + 5 < 7 Subtract 5 from each side 𝑥 −2 < 2 Multiply each side by -2. ∙ -2 ∙ -2 x>-4 Don’t forget to flip the sign! Graph.