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Chapter 0: Problem 127

What is a compound inequality and how is it solved?

Short Answer

Expert verified
A compound inequality is a sentence with two inequality statements joined either by 'and' or 'or'. To solve 'and' compound inequalities, find the intersection of the solutions of both inequalities. To solve 'or' compound inequalities, find the union of the solutions for both inequalities.

Step by step solution

01

Definition of Compound Inequality

A compound inequality is a sentence with two inequality statements joined either by the word 'or' or by the word 'and.' 'And' indicates that both inequalities must hold true at the same time. 'Or' suggests that at least one of the inequalities must be true.
02

Solving 'And' Compound Inequalities

For a compound inequality joined by 'and', the solution is the intersection of the solutions for both inequalities. For instance, 1 < x 'and' x < 3. You solve each inequality separately (x > 1 and x < 3) and then find where the solutions overlap. This gives the solution 1 < x < 3.
03

Solving 'Or' Compound Inequalities

For a compound inequality joined by 'or', the solution is the union of the solutions for both inequalities. Such as: x < -2 'or' x > 3. You solve each inequality separately (x < -2 and x > 3). In this case, their union will be the solution: x < -2 or x > 3. This means that 'x' is a solution if it makes either one of the inequalities (or both) true.

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Most popular questions from this chapter

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