1.5 Solving Absolute Value Inequalities

An absolute value inequality is an inequality that involves the absolute value of a variable expression, indicating the distance of the expression from zero on a number line.

It means that the value of x is within a distance of a from 0, resulting in the compound inequality -a < x < a.

It means that the value of x is more than a distance of a from 0, resulting in the compound inequalities x < -a or x > a.

No Solution, because absolute values cannot be negative.

-5 < w < 6.

All Real Numbers, because absolute values are always non-negative.

No Solution, because absolute values cannot be negative.

It represents the values of x that are within 3.5 units from 0, resulting in the compound inequality -3.5 ≤ x ≤ 3.5.

Set up the compound inequality -a < x < a and solve for x.

Set up the compound inequalities x < -a or x > a and solve for x.