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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

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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, .12

345 x

Write the solution set in interval notation.

The solution set is [ - 7/4, 1/4].

Table of Contents

Compound Linear Inequalities: Solving Algebraically