Absolute Value Inequality Solver

All math tools

Solve inequalities of the form |ax + b| < c or |ax + b| > c.

Equation Parameters

Coefficient (a)

Constant (b)

|1x+0|<5

Inequality Relation

Inclusion Type

Limit (c)

Solution Region

(-5.00, 5.00)

Interval Notation

Lower Bound-5.00

Upper Bound5.00

Verbal DescriptionAll values between -5.00 and 5.00

-10

-5

Solution Path

1.Setup: -5 < 1x + 0 < 5

2.Subtract 0: -5.00 < 1x < 5.00

3.Divide by 1: -5.00 < x < 5.00

About this calculator

Understanding |ax + b| < c

Solving absolute value inequalities depends on the direction of the inequality sign. A 'less than' (<) sign implies the expression is sandwiched between -c and c (an 'AND' statement). A 'greater than' (>) sign implies the expression is outside the range -c to c (an 'OR' statement).

💡

Pro Tips

If c is negative and you have |x| < c, there is No Solution.
If c is negative and you have |x| > c, the solution is All Real Numbers.
Remember to flip the inequality sign when dividing by a negative number 'a'.

Fun Facts

"These inequalities are the backbone of defining 'limits' in calculus using epsilon-delta definitions."
"In manufacturing, |x - target| ≤ tolerance defines the acceptable range for a product's dimensions."
"Visually, 'less than' represents the interior of a segment, while 'greater than' represents the two rays pointing away from each other."