Solve inequalities of the form |ax + b| < c, > c, ≤ c, ≥ c
|ax + b| ? c
This calculator helps you solve absolute value inequalities of the form |ax + b| < c, |ax + b| > c, |ax + b| ≤ c, and |ax + b| ≥ c. Simply enter the coefficient a, constant b, inequality sign, and value c, and the calculator computes the solution instantly.
Input your inequality values easily:
The calculator dynamically updates the inequality formula as you type.
The calculator solves absolute value inequalities efficiently:
No manual calculation is needed – get instant and accurate results.
Understand the inequality structure:
This helps beginners learn the step-by-step reasoning behind absolute value inequalities.
Results update in real-time as you type:
Follow these simple steps to use the calculator effectively:
This step-by-step process allows both beginners and advanced users to quickly solve inequalities without manual calculation, while also learning the logic behind absolute value inequalities.
Absolute value inequalities involve expressions of the form |ax + b| ? c, where a is the coefficient of x, b is a constant, c is the value on the right-hand side, and ? represents an inequality sign (<, ≤, >, ≥). The absolute value ensures that the expression inside the bars is always non-negative. To solve such inequalities, we break them into two linear inequalities based on the definition of absolute value.
|ax + b| < c ⇒ -c < ax + b < c
|ax + b| ≤ c ⇒ -c ≤ ax + b ≤ c
|ax + b| > c ⇒ ax + b < -c OR ax + b > c
|ax + b| ≥ c ⇒ ax + b ≤ -c OR ax + b ≥ c
Steps to solve these inequalities:
Suppose you have the inequality:
|2x − 3| < 5
The calculator computes:
−1.00 ≤ x ≤ 4.00
Change any coefficient, constant, or inequality sign to see instant updates and understand how solutions vary with different values.
Learn how to solve inequalities of the form |ax + b| < c, > c, ≤ c, or ≥ c quickly and accurately.
It solves absolute value inequalities of the form |ax + b| < c, > c, ≤ c, or ≥ c. Enter the coefficients and inequality, and it gives the solution instantly.
Yes! It is completely free to use with no registration or hidden charges.
You need to enter the coefficient of x (a), the constant term (b), the inequality sign (<, ≤, >, ≥), and the value on the right-hand side (c). The calculator computes the solution automatically.
Yes, the calculator supports positive, negative, and zero values for all inputs, except the coefficient 'a', which cannot be zero.
If the inputs create an impossible inequality (e.g., |ax + b| < c with c < 0), the calculator will display “No solution.”
Yes, use the “Clear All” button to reset inputs or the “Reload Calculator” button to reload the page completely.
Yes, the calculator dynamically displays the formula |ax + b| ? c as you enter values, helping you verify the inequality before solving.
Yes, the calculator is fully responsive and works smoothly on smartphones, tablets, laptops, and desktops.
Solutions are calculated and displayed with up to two decimal places, ensuring clarity and accuracy for all inequality types.
Students, teachers, or anyone learning algebra can use it to solve absolute value inequalities quickly, check homework, or understand solution methods.
Explore more algebra calculators, tools, and guides to simplify polynomial, equation, and expression problems quickly and accurately.