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Chapter 1: Problem 137

What is a compound inequality and how is it solved?

Short Answer

Expert verified
A compound inequality is an equation with two or more inequalities joined together with either 'and' or 'or'. It's solved by simplifying and solving the inequalities separately, then finding the intersection ('and') or union ('or') of the solutions.

Step by step solution

01

Understand the Problem

A compound inequality involves two inequalities. Inequalities use the symbols <, 鈮�, >, 鈮� to show the relative positions of quantities. 'And' is used to denote the intersection of two sets, i.e., x is in this set AND that set. 'Or', on the other hand, is used to denote the union of two sets, i.e., x is in this set OR that set. Here, you need to understand the problem and be able to differentiate between intersection and union.
02

Simplify the equation

Next, simplify the inequalities separately by adding, subtracting, multiplying or dividing. In the case of multiplication or division by a negative number when dealing with inequalities, the inequality symbol should be reversed.
03

Find the solution

After simplifying the inequalities, solve them separately to find the potential values of the variable. The solution for 'and' (intersection) is the set of points that satisfy both conditions, i.e., the overlap of both solutions. For 'or' (union), the solution is either one of the solutions or both.
04

Interpret the results

Present your answer. If the compound inequality is an 'and' solution, generally the answer is written like 'a < x < b'. If it's an 'or' solution, the answer is displayed as two separate inequalities, e.g., 'x < a or x > b'.

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