Question

Using an absolute-value inequality, describe the set of numbers whose distance from 4 is greater than 5 units. Draw a graph of this set on a number line. Finally, describe this set of numbers using inequalities without absolute value signs.

Answer 1

The solution to the absolute-value inequality is x > 9; and x < -1

What is an inequality?

An inequality is an expression that shows the nonequal comparison of two or more numbers and variables.

Let x represent the unknown number, hence:

|x - 4| > 5

(x - 4) > 5; and -(x - 4) > 5

x > 9; and x < -1

The solution to the absolute-value inequality is x > 9; and x < -1

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