This document provides an overview of inequalities and how to solve them algebraically. It discusses representing inequalities on number lines, and the rules for adding, subtracting, multiplying, and dividing terms when solving inequalities, such as changing the sign of the inequality when multiplying or dividing by a negative number. Examples are provided of solving inequalities algebraically and representing the solutions on number lines.

2. Inequalities
By the end of this lesson you will be able to:
• Read and represent inequalities.
• Solve inequalities algebraically.

3. inequalities

4. n is less than 3
x is greater than or
equal to 8
a is less than or equal
to ­5
n < 3
x ≥ 8
a ≤ ‐5

5. is equivalent to
x is greater than 3 but
less than 8
a is greater than ­4 but
less than or equal to 9
3 < 6
3 < x < 8
‐4 < a ≤ 9
6 > 3

6. Represent the inequalities on the number line.

7. Represent the inequalities on the number line.

8. + 7 + 7
In an inequality , you can add he same number to
both sides and the inequality remains true.

9. In an inequality , you can subtract the same number
to both sides and the inequality remains true.
‐3 ‐3

10. In an inequality , you can multiply by the same
positive number both sides and the inequality
remains true.
x3 x 3

11. In an inequality , you can divide by the same
positive number both sides and the inequality
remains true.
÷2 ÷2

12. What happens if you multiply the inequality by a
negative number ?
x (‐1) x (‐1)

13. What happens if you divide the inequality by a
negative number ?
÷ (‐2) ÷ (‐2)

14. When you multiply or divide an
inequality by a negative number,
the sign must be changed around.

15. Solve the inequality and represent the solution on a
number line.
15 + 3 x < 6

16. Solve the inequality and represent the solution on a
number line.
18 ≤ 7x + 4

17. Solve the inequality and represent the solution on a
number line.
19 ­ 4 x ≥ 3

18. Solve the inequality and represent the solution on a
number line.
4 ­ 5 x ≥ 2x ­ 3

19. 3 ( x ­ 1 ) < 2 ( 1 ­ x )

20. 2( x ­ 1 ) > x ­ 7

23. Solve from Book : pages 62 & 63