Inequality Calculator
Solve linear, quadratic and absolute value inequalities step-by-step. The calculator shows the work and graphs the solution on a number line.
How to Use the Calculator
- Type your inequality in the box above
- Select the type of inequality (optional, the calculator will try to detect it)
- Click "Solve" to get the solution
- The solution will be displayed with step-by-step explanation and a number line graph
Solution: -
Enter an inequality to see the solution and step-by-step explanation.
About Inequality Calculator
This inequality calculator solves linear, quadratic, and absolute value inequalities, showing the solution as an inequality, interval notation, and on a number line. The calculator also provides step-by-step explanations to help you understand how to solve inequalities.
Types of Inequalities
The calculator can solve the following types of inequalities:
- Linear inequalities: Inequalities with linear expressions (e.g., 2x + 3 < 5)
- Quadratic inequalities: Inequalities with quadratic expressions (e.g., x² - 4 > 0)
- Absolute value inequalities: Inequalities with absolute value expressions (e.g., |2x - 3| >= 7)
How to Solve Inequalities
The general approach to solving inequalities is similar to solving equations, with one important exception: when multiplying or dividing both sides of an inequality by a negative number, you must reverse the inequality sign.
Solving Linear Inequalities
1. Isolate the variable on one side of the inequality
2. Perform the same operations on both sides
3. Remember to reverse the inequality sign when multiplying/dividing by a negative number
Solving Quadratic Inequalities
1. Move all terms to one side to set the inequality to zero
2. Find the roots of the corresponding equation
3. Test intervals between the roots to determine where the inequality holds true
Solving Absolute Value Inequalities
1. Isolate the absolute value expression
2. For |A| < B, rewrite as -B < A < B
3. For |A| > B, rewrite as A < -B or A > B
Examples
Example 1: Solve 3x + 4 > 10
Subtract 4 from both sides: 3x > 6
Divide both sides by 3: x > 2
Example 2: Solve x² - 5x + 6 < 0
Factor: (x-2)(x-3) < 0
Roots at x=2 and x=3
Test intervals: Solution is 2 < x < 3
Example 3: Solve |2x - 5| >= 3
Rewrite as: 2x - 5 <= -3 or 2x - 5 >= 3
Solve both: x <= 1 or x >= 4