1. Inequalities
Note: Pretend the inequality sign is an = sign until the very last step
Natural Numbers (N)
Integers (Z)
Real Numbers (R)

2. Symbols Less than Greater than Less than OR EQUAL TO
Greater than OR EQUAL TO

3. Draw x > x N
Draw x x Z
Draw x x R

4. Solutions…. You can have a range of answers……
All real numbers less than 2
x< 2

5. Solutions continued… -5 -4 -3 -2 -1 0 1 2 3 4 5
All real numbers greater than -2
x > -2

6. Solutions continued…. -5 -4 -3 -2 -1 0 1 2 3 4 5
All real numbers less than or equal to 1

7. Solutions continued… -5 -4 -3 -2 -1 0 1 2 3 4 5
All real numbers greater than or equal to -3

8. Solving an Inequality x < 8 Solve using addition: x – 3 < 5
Add the same number to EACH side.
x < 8

9. Solving Using Subtraction
Subtract the same number from EACH side.

10. Using Subtraction…
Graph the solution.

11. Using Addition…
Graph the solution.

12. Solving using Multiplication
Multiply each side by the same positive number.
(2)

13. Solving Using Division
Divide each side by the same positive number. 3

14. Solving by dividing by a negative #-2

15. Solving by multiplication of a negative #
Multiply by (-1).
(-1)

16. When you multiply or divide each side of an inequality by a negative number, you must reverse the inequality symbol

18. Show x > 2 on a number line
Example 1
Show x > 2 on a number line
Answer: This means all numbers bigger than 2 -4 -3 -2 -1 1 2 3 4 5
Example 2
Show x ≤ 3 on a number line
Answer: This means all numbers less than and including 3
Example 3
Show -2 < x ≤ 1 on a number line -4 -3 -2 -1 1 2 3 4 5
Answer: This means all numbers between -2 and 1
including 1 but not -2
Continue
Teaching 2
Monday, 20 May 2019 -4 -3 -2 -1
By Cang Tu 1 2 3 4 5
1st Slide

19. Worksheet 1 For each question, show the inequality on the number line
Grade C
Qu1-2
For each question, show the inequality on the number line
x > 1
x ≤ 3
x ≤ -1
1 < x ≤ 4
-2 ≤ x < 2 -4 -3 -2 -1 1 2 3 4 5 -4 -3 -2 -1 1 2 3 4 5 -4 -3 -2 -1 1 2 3 4 5 -4 -3 -2 -1 1 2 3 4 5 -4 -3 -2 -1
Write an the inequality for each diagram a) b) c) 1 2 3 4 5 -4 -3 -2 -1 1 2 3 4 5 -4 -3 -2 -1 1 2 3 4 5
WS 2
Monday, 20 May 2019 -4 -3 -2 -1 1 2 3 4 5
1st Slide

20. Grade C
Qu1-7
Worksheet 2
Find the solutions of these inequalities and show it on a number line
3x + 2 > 8
5x – 3 ≤ 12
2x – 7 < 1
2x - 3 > 0
3(2x + 1) ≥ 9
3x – 1< x + 5
4(x - 1) ≥ 2x – 3 -1 -2 -3 -4 1 2 3 4 5 -1 -2 -3 -4 1 2 3 4 5 -1 -2 -3 -4 1 2 3 4 5 -1 -2 -3 -4 1 2 3 4 5 -1 -2 -3 -4 1 2 3 4 5 -1 -2 -3 -4 1 2 3 4 5 -1 -2 -3 -4 1 2 3 4 5
Monday, 20 May 2019
By Cang Tu
1st Slide

21. Short Method Solve the compound inequality and graph the solutions.
8 < 3x – 1 ≤ 11
1. add 1 to each part of the inequality.
8 < 3x – 1 ≤ 11
9 < 3x ≤ 12
2. divide each part of the inequality by 3 to undo the multiplication.
3 < x ≤ 4
The solution set is {x:3 < x ≤ 4}.

22. Solve –3 < –1 – 2x ≤ 5. Then graph the solution.
Example 5
Reversing the sign
Solve –3 < –1 – 2x ≤ 5. Then graph the solution.
–2 < – 2x ≤ 6
Reverse the inequalities when you divide by a negative
– – –2
1 > x ≥ –3

23. Try these Solve and graph the inequality. 1. 2. 3. -2 -1 0 1 2 3 4 5 6 2. 3.

24. Match the Compound Inequality with the Correct Graph
0 < x + 2 < 5
-4 + a > 1 OR -4 + a < -3
-3 < x + 2 < 3
2 < x + 2 < 5
x + 2 < -6 OR x + 2 > -2 -8 -6 -4 -4 -2 -2 2 1 3 5 2 4

25. Now You Try… Solve and Graph the Compound Inequality
-3 < x + 2 < 7
x – 1 < -1 OR x – 5 > -1
2 < x + 2 < 5
11 < 2x + 3 < 21
n + 2 < 3 OR n + 3 > 7 -5 5
-5 < x < 5 2 4
x < 0 OR x > 4 2 4
0 < x < 3 4 6 8
4 < x < 9
x < 1 OR x > 4 1 3 5