1. INEQUALITIES

2. Inequalities < less than ≤ less than or equal to > greater than
Signs used in inequalities are…
< less than
≤ less than or equal to
> greater than
Ask the participants to explain the difference between the signs.
≥ greater than or equal to

3. Inequalities This means all numbers less than four. x < 4
open circle
Since 4 is not less than 4 than 4 we can not include the 4. To show that the 4 is not included we put an open circle on the 4. Then show an arrow in the directions for numbers less than 4. (3, 2, 1, 0, -1, …). We use an arrow because this is an infinite set of numbers.

4. Inequalities This means all numbers greater than -2. x > -2
open circle
Ask the participants which numbers are greater than -2. (-1, 0, 1…) So the direction of the arrow is to the right.
Remind the participants that the -2 is NOT included.

5. Inequalities This means all numbers less than or equal to -1 x ≤ -1
closed circle
Notice you want all numbers greater than or equal to -1. To show that this time we want to include the -1. We use a CLOSED OR SHADED IN CIRCLE.

6. Inequalities This means all numbers greater than or equal to -4 x ≥ -4
closed circle
Ask the participants which numbers are greater than 4. (-3, -2, -1, 0, 1…) So the direction of the arrow is to the right.
Remind the participants that the -2 is NOT included.

7. Inequalities
When solving one-step inequalities that involve addition or subtraction you follow the same rules as solving equations.
Stress that in these cases you follow the same procedure as you would when solving equations.

8. Inequalities
When solving one-step inequalities that involve multiplication or division by a POSITIVE NUMBER you follow the same rules as solving equations.
Again stress you follow the same procedures as you would when solving equations.

9. 5 < 7 (-1)5 < 7(-1) -5 < -7 -5 > -7 Inequalities
What happens when you multiply or divide an equality by a negative number.
5 < 7
Lets start with this.
(-1)5 < 7(-1)
Multiply both sides by -1
This statement is incorrect. To make it correct we need to “flip” the inequality sign.
-5 < -7
Do several examples with the participants.
-5 > -7
CORRECT

10. 30 > 15 -5 -5 -6 > -3 -6 < -3 Inequalities Start here
Start here
Divide both sides by -5
-6 > -3
This answer is incorrect.
Explain and show to the participants that on the number line 7 is greater than 5 but -7 is less than -5.
-6 < -3
To make it correct we need to “flip” the sign.

11. Lets state a rule to follow when we multiply or divide an inequality by a negative number.
How about, when you multiply or divide an inequality by a negative number, “flip” the sign.

12. -5x + 6 > 61 -5x + 6 - 6 > 61-6 -5x > 55 -5 -5 x < -11
Inequalities
-5x + 6 > 61
-5x > 61-6
-5x > 55
Walk the participants through each step. Reminding them that in the last step we flipped the sign because we divided by a negative.
Tell the participants we will now check to see if the answer is correct.
x < -11
Lets check this answer to see if it is correct.

13. x < -11 -5x + 6 > 61 -5(-20) + 6 > 61 100 + 6 > 61
Inequalities
x < -11
All numbers less than -11.
-20
Pick a number less than -11
-5x + 6 > 61
Substitute this number in the problem and then simplify
-5(-20) + 6 > 61
> 61
106 > 61
Correct..it works!