Absolute Value Inequalities

An inequality that contains an absolute value expression, which represents the distance of a number from zero on the number line.

You can isolate the absolute value by performing inverse operations, such as adding, subtracting, multiplying, or dividing both sides of the inequality.

It means that x is within a distance of a from 0, or -a < x < a.

It means that x is outside the distance of a from 0, or x < -a or x > a.

You create two inequalities: x - 4 > 5 or x - 4 < -5, which simplifies to x > 9 or x < -1.

Isolate the absolute value by setting up the inequalities: -7 < 2x + 3 < 7.

The solution is -5 < x < 1.

The solution is x < -3 or x > 5.

The solution represents a range of values that satisfy the inequality, indicating where the variable lies in relation to a certain distance.

It means that there are no values of the variable that can satisfy the inequality.