1. Table of Contents Compound Linear Inequalities: Solving Algebraically Example: Algebraically solve, - 5 < 2x + 3  8. First break the compound inequality into two simple inequalities by writing it as: 2x + 3 > - 5 and 2x + 3  8 Next solve each simple inequality. The "and" means that only those numbers that satisfy both of the inequalities will be solutions of the original compound inequality. x > - 4 and x  5/2 2x > - 8 and 2x  5

2. Table of Contents Compound Linear Inequalities: Solving Algebraically Slide 2 x > - 4 and x  5/2 Numbers that satisfy both inequalities above are between -4 and 5/2 (including 5/2). The solution set can be written as a compound inequality, - 4 < x  5/2 or in interval notation as ( - 4, 5/2 ]. Try: Algebraically solve, Write the solution set in interval notation. The solution set is [ - 7/4, 1/4].

3. Table of Contents Compound Linear Inequalities: Solving Algebraically