This document discusses multi-step and compound inequalities. It provides examples of solving multi-step inequalities by combining like terms and then solving for x. It also explains that for compound inequalities using "and", both inequalities must be true, and the solution set is the intersection of the two individual inequalities. An example of graphing the solution set of -1 < x < 2 is given.

6. Multi-Step & Compound Inequalities

43. Multi-Step Inequalities
1. 3x -2(6x - 4) > 4 - (4x + 6)
1. 3x -12x + 8 > -2 - 4x; -5x > -10;
2. 6x - 4 < 2x + 12
2. 4x < 16
x<4
3. 3x - 15 > 4 + 5x
3. -2x > 19;
4.
x < - 19/2; x < - 9 1/2
x<2

44. Class Work:
See Handout

46. Compound Inequalities
If a compound inequality uses 'and', both inequalities
must be true. The solution set is the intersection of the
two inequalities.
1. Graph the solutions set of x < 2 and x > -1
The solution set is therefore: { x| -1 < x < 2}