1. INEQUALITIES Many Kinds of Inequalities : Linear Inequalities
Quadratic Inequalities
Fractional Inequalities
Irrational Inequalities
Absolute Value Inequalities

2. 1. LINEAR INEQUALITIES The Sign of Can be : >, <, ≤, ≥, ≠
General Form : ax + b > 0
Example :
Find The solution Set :
a. 2x -3 > 7
b. 5 (x+1) ≥ 2 ( x +7)
c. -2 < 3x -5 ≤ 4 d.

3. Solution : a. 2x- 3 > 7 2x > 7 + 3 2x > 10 x > 5
a Line Graph of Solution Set : ●
0 5 ss
Solution Set is = { x/ x > 5, x Є R }

4. Solution b. 5(x+1)≥ 2 (x +7) 5x + 5 ≥ 2x +14 5x -2x ≥ 14 -5 3x ≥ 9
a line the graph of solution set is : ss
Solution Set is = { x/ x ≥ 3, x Є R }

5. Solution
c. -2 < 3x-5 ≤ 4
-2 +5 < 3x ≤ 4 + 5
3 < 3x ≤ 9
3/3 < 3x/ ≤ 9/3
1 < x ≤ 3
a line graph of solution is : ss
Solution Set is { x/x 1 < x ≤ 3, x Є R }

6. Solution SS d. 3(x-3) < 8 3x -9 < 8 3x < 17 x < 17/3
a line graph of solution is : /3 SS
Solution set is { x/x < 17/3, x Є R }