Absolute Value (or modulus) is the value of a number without regard to its sign. The absolute value of any number is always positive or zero.
a = a, if a ≥ 0
a = a, if a < 0
For example, x = 5 indicates that x = 5 or –5.
Properties of Absolute Value

a = √a^{2}

a ≥ 0

a = 0 if and only if a = 0

a = a

a+b ≤ a + b

a ≤ b iff b ≤ a ≤ b

a ≥ b iff a ≤ b or b ≤ a
Absolute Value and Inequalities
If a < b, then there are two cases:
 a < b
 a < b
In the first case, remove the absolute value brackets and solve. In the second case, remove the absolute value brackets, put a negative sign on the other side of the inequality, and change the sign.