Solution of an Inequality


The solution of an inequality is any number that makes the inequality true. For example, 5 is a solution of the inequality x < 6 since 5 is smaller than 6 and -4 is also a solution of x < 6 since -4 is smaller than 6.

In fact, the solutions of the inequality x < 6 are all numbers that are smaller than 6.

A couple of examples showing how to find a solution of an inequality


Example #1

Find a solution of x + 2 < 5

Subtract 2 from each side of the inequality

x + 2 - 2 < 5 - 2

x < 3

A solution of x < 3 is -4

Example #2

Find a solution of 3x - 1 > 5

Add 1 to each side of the inequality

3x - 1 + 1 > 5 + 1

3x > 6

Divide each side by 3

3x / 3 > 6 / 3

x > 2

A solution x > 2 is 10

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