Solving Absolute Value Equations and Inequalities
Let k be a positive real number, and p and q be real numbers.
1. To solve │ ax + b│=k, solve the compound equation
ax + b = k or ax + b = –k.
The solution set is usually of the form {p, q}, which includes two
2. To solve │ ax + b│ > k, solve the compound inequality
ax + b > k or ax + b < – k.
The solution set is of the form (-∞, p) U (q,∞), which consists of
two separate intervals.
3. To solve │ ax + b│ < k, solve the three-part inequality
– k < ax + b < k.
The solution set is of the form ( p, q), a single interval.
