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

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.

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 }

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 : 0 3 ss Solution Set is = { x/ x ≥ 3, x Є R }

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

Solution SS d. 3(x-3) < 8 3x -9 < 8 3x < 17 x < 17/3 a line graph of solution is : 0 17/3 SS Solution set is { x/x < 17/3, x Є R }