1. Inequalities

2. SymbolMeaning <Less Than >Greater Than =Equal <Less Than or Equal To >Greater Than or Equal To

3.  A number line ex:  A variable ex: x, y, v, z, etc.  To Shade ex:  Shade all solutions that make the inequality true! Do NOT shade the direction of the sign! Instead, only shade where the solutions are true.

4.  Step 1: Determine a solution that makes the inequality true.  Does 5 work? Substitute 5 for the variable and check.  5 < 5 This is false, so 5 does not work.  Does 6 work? Substitute 6 for the variable and check.  6 < 5. This is false, so 6 does not work.  Does 4 work? Substitute 4 for the variable and check.  4 < 5. This is true, so 4 does work !  Step 2: Draw a number line and the shade the side where all of the values make the inequality true.  4 is a value that works & is located on the left of 5 on the number line. Shade on the left. 5

5.  Step 1: Determine a solution that makes the inequality true.  Does 5 work? Substitute 5 for the variable and check.  5 < 5 This is false, so 5 does not work.  Does 6 work? Substitute 6 for the variable and check.  5 > 6. This is false, so 6 does not work.  Does 4 work? Substitute 4 for the variable and check.  5 > 4. This is true, so 4 does work !  Step 2: Draw a number line and the shade the side where all of the values make the inequality true.  4 is a value that works & is located on the left of 5 on the number line. Shade on the left. 5

6. x x! Although the signs point in different directions, for these inequalities, the solutions that make the inequalities true are on the left of 5 on the number line.

7. Do NOT shade the direction of the sign! Instead, only shade the side where the solutions are true. > does not always mean shade on the right! < does not always means shade on the left!

8.  Step 1: Determine a solution that makes the inequality true.  Does 5 work? Substitute 5 for the variable and check.  5 > 5 This is false, so 5 does not work.  Does 4 work? Substitute 4 for the variable and check.  4 > 5. This is false, so 4 does not work.  Does 6 work? Substitute 6 for the variable and check.  6 > 5. This is true, so 6 does work !  Step 2: Draw a number line and the shade the side where all of the values make the inequality true.  6 is a value that works & is located on the right of 5 on the number line. Shade on the right. 5

9.  Step 1: Determine a solution that makes the inequality true.  Does 5 work? Substitute 5 for the variable and check.  5 < 5 This is false, so 5 does not work.  Does 4 work? Substitute 4 for the variable and check.  5 < 4. This is false, so 4 does not work.  Does 6 work? Substitute 6 for the variable and check.  5 < 6. This is true, so 6 does work !  Step 2: Draw a number line and the shade the side where all of the values make the inequality true.  6 is a value that works & is located on the right of 5 on the number line. Shade on the right. 5

10. x > 5 has the same graph as 5 < x! Although the signs point in different directions, for these inequalities, the solutions that make it true are on the right of 5 on the number line.

11. Do NOT shade the direction of the sign! Instead, only shade the side where the solutions are true. > does not always mean shade on the right! < does not always means shade on the left!

12.  Step 1: Determine a solution that makes the inequality true.  Does 5 work? Substitute 5 for the variable and check.  5 < 5 This is true, so 5 does work.  Does 6 work? Substitute 6 for the variable and check.  6 < 5. This is false, so 6 does not work.  Does 4 work? Substitute 4 for the variable and check.  4 < 5. This is true, so 4 does work !  Step 2: Draw a number line and the shade where all of the values make the inequality true. Also shade the circle, as the solution can also be 5!  4 is a value that works & is located on the left of 5 on the number line. Shade on the left. 5

13.  Step 1: Determine a solution that makes the inequality true.  Does 5 work? Substitute 5 for the variable and check.  5 > 5 This is true, so 5 does work.  Does 6 work? Substitute 6 for the variable and check.  5 > 6. This is false, so 6 does not work.  Does 4 work? Substitute 4 for the variable and check.  5 > 4. This is true, so 4 does work !  Step 2: Draw a number line and the shade the side where all of the values make the inequality true. Also shade the circle, as the solution can also be 5!  4 is a value that works & is located on the left of 5 on the number line. Shade on the left. 5

14. x x! Although the signs point in different directions, for these inequalities, the solutions that make it true are on the left of 5 on the number line.

15. Do NOT shade the direction of the sign! Instead, only shade the side where the solutions are true. > does not always mean shade on the right! < does not always means shade on the left!

16.  Step 1: Determine a solution that makes the inequality true.  Does 5 work? Substitute 5 for the variable and check.  5 > 5 This is true, so 5 does work.  Does 4 work? Substitute 4 for the variable and check.  4 > 5. This is false, so 4 does not work.  Does 6 work? Substitute 6 for the variable and check.  6 > 5. This is true, so 6 does work !  Step 2: Draw a number line and the shade the side where all of the values make the inequality true. Also shade the circle, as the solution can also be 5!  6 is a value that works & is located on the right of 5 on the number line. Shade on the right. 5

17.  Step 1: Determine a solution that makes the inequality true.  Does 5 work? Substitute 5 for the variable and check.  5 < 5 This is true, so 5 does work.  Does 4 work? Substitute 4 for the variable and check.  5 < 4. This is false, so 4 does not work.  Does 6 work? Substitute 6 for the variable and check.  5 < 6. This is true, so 6 does work !  Step 2: Draw a number line and the shade the side where all of the values make the inequality true. Also shade the circle, as the solution can also be 5!  6 is a value that works & is located on the right of 5 on the number line. Shade on the right. 5

18. x > 5 has the same graph as 5 < x! Although the signs point in different directions, for these inequalities, the solutions that make it true are on the right of 5 on the number line.

19. Do NOT shade the direction of the sign! Instead, only shade the side where the solutions are true. > does not always mean shade on the right! < does not always means shade on the left!

20. OPEN CIRCLECLOSED CIRCLE << >> =

21. 1. x + 1 = 5 for x = 4 _________________ 2. 13 - w = 10 for w = 2 ________________ 3. 2 v = 12 for v = 10 _________________ 4. 14 ÷ p = 2 for p = 7 _________________ 4 + 1 = 5 yes 14 ÷ 7 = 2 yes 2 ∙ 10 ≠ 12 no 13 - 2 ≠ 10 no

22. 1. w  0 0 2. b   4 -4 3. j > 5 5 4. 6 > q 6