Solving Absolute Value Inequality

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Oct 31st, 2015

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|x + 2| + 5 < 1

Subtract 5 from both sides

|x + 2| + 5 - 5 < 1 - 5

|x + 2| < -4

The above equation is saying that absolute value of x + 2 is a negative number less than -4.

But absolute value of a number can never be negative.

(The absolute value or modulus |x| of a real number x is the non-negative value of x without regard to its sign. The absolute value of a number may be thought of as its distance from zero in the number line).


Hence, this inequality equation does not have any solution(i.e. there are no values of x that make the equation true).

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Oct 31st, 2015

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