Word Problem Inequality Solver Calculator

Calculator Form

Use auto mode for word problems or manual mode for direct inequality entry.

Word Problem

Input Mode

Variable

Decimal Precision

Coefficient (a)

Constant (b)

Operator

Right Side Value (c)

Graph Span

Manual model used: ax + b [operator] c. Auto mode works best for common school-style, single-variable statements.

Example Data Table

Word Problem	Translated Inequality	Solved Form
Twice a number increased by 5 is at least 17.	2x + 5 ≥ 17	x ≥ 6
A number minus 4 is less than 10.	x - 4 < 10	x < 14
Three times a number is no more than 21.	3x ≤ 21	x ≤ 7
Five less than a number is greater than 8.	x - 5 > 8	x > 13
Half of a number plus 6 is at most 15.	0.5x + 6 ≤ 15	x ≤ 18

Formula Used

The calculator models common word problems as a one-variable linear inequality:

ax + b [operator] c

Here, a is the coefficient, b is the constant added or subtracted, and c is the right-side boundary value.

Solving method:

Move the constant: ax [operator] c - b
Divide by the coefficient: x [operator] (c - b) / a
If you divide by a negative coefficient, reverse the inequality sign.

How to Use This Calculator

Enter the word problem in the large text area.
Select Auto parse to let the tool translate common verbal phrases.
Or choose Manual inequality entry and fill in coefficient, constant, operator, and right-side value.
Set the variable name, decimal precision, and graph span.
Click Solve Inequality to display the result above the form.
Review the steps, interval notation, verification table, and Plotly graph.
Use the CSV or PDF buttons to export your result.

Frequently Asked Questions

1. What does this calculator solve?

It solves one-variable linear inequalities written directly or described in everyday language. It also shows interval notation, set-builder notation, a graph, and checking values.

2. What phrases can auto mode usually understand?

It commonly detects phrases like at least, at most, more than, less than, sum of, minus, increased by, decreased by, product of, and quotient of.

3. Why does the inequality sign sometimes flip?

When both sides are divided by a negative number, the direction reverses. That keeps the statement mathematically equivalent and preserves the correct solution set.

4. Can I enter decimals or negative values?

Yes. The coefficient, constant, and right-side boundary all accept decimals and negative numbers, so you can test many classroom and homework scenarios.

5. What does interval notation tell me?

Interval notation gives a compact way to describe every solution value on the number line. Brackets include boundaries, while parentheses exclude them.

6. What if auto parsing misses my wording?

Switch to manual mode and enter the inequality directly as ax + b compared with c. That guarantees a clean result even for unusual wording.

7. What is the verification table for?

It tests several x-values around the boundary, evaluates the left side, and shows whether each value makes the original inequality true or false.

8. Does the graph show included and excluded boundaries?

Yes. A filled marker represents an included endpoint, and an open marker represents an excluded endpoint. The highlighted ray shows the valid solution side.