Advanced Multi Step Inequality Calculator

Enter both sides, choose a sign, solve carefully. Review algebra steps, interval notation, and graphs. Make inequality practice easier across classes, tutoring, and homework.

Calculator Input

This solver supports linear expressions with parentheses, decimals, fractions, and implicit multiplication such as 3(x-2). It does not solve nonlinear terms like x² or x(x+1).

Example Data Table

Inequality Simplified Form Solution Interval
3(x − 2) + 5 ≤ 2x + 7 x ≤ 8 x ≤ 8 (-∞, 8]
4 − 2(x + 3) > 10 − 5x 3x > 12 x > 4 (4, ∞)
(5x − 7)/3 ≥ 2x + 1 -x ≥ 10 x ≤ -10 (-∞, -10]
7 − (x − 4) < 2(3 − x) x < -5 x < -5 (-∞, -5)

Formula Used

For a linear inequality of the form ax + b ? cx + d, first move variable terms together and constants together.

ax + b ? cx + d → (a − c)x ? (d − b)

After that, divide by the coefficient of the variable to isolate it. When you divide or multiply by a negative value, reverse the inequality sign.

If k < 0, then ax ? b becomes x > b/a when the original sign was <, and similarly for the other signs.

How to Use This Calculator

  1. Type the left expression exactly as it appears.
  2. Select the correct inequality sign.
  3. Type the right expression using the same variable.
  4. Use parentheses when distribution is needed.
  5. Press Solve Inequality to see the answer, interval notation, work steps, and graph.
  6. Use the export buttons to save the solved result as CSV or PDF.

FAQs

1. What types of inequalities can this page solve?

It solves linear multi step inequalities with one variable. You can use parentheses, decimals, fractions, and implicit multiplication like 2(x−3). Nonlinear forms such as x², x(x+1), or x/(x−1) are outside this solver’s scope.

2. Why does the inequality sign sometimes flip?

The sign flips whenever you divide or multiply both sides by a negative number. That rule keeps the inequality statement true. The calculator highlights that step so you can see exactly when and why the direction changes.

3. Can I enter decimals and fractions?

Yes. You can enter decimals like 2.5x − 1.2 and fractions written with division, such as (3x−5)/4. Use parentheses around grouped numerators or denominators to keep the expression clear.

4. What does interval notation mean here?

Interval notation shows the complete solution set on the number line. Parentheses mean the endpoint is excluded. Brackets mean the endpoint is included. The graph and the interval notation always match the final solved statement.

5. What happens if both variable terms cancel?

When variable terms cancel, the result becomes either always true or always false. That means the answer is either all real numbers or no real numbers. The calculator checks that final constant comparison automatically.

6. Does the graph replace algebra steps?

No. The graph is a visual summary. The calculator still shows simplified expressions and isolation steps so you can follow the algebra. This makes it useful for checking homework, teaching, tutoring, and self practice.

7. Why did I get an unsupported expression message?

That message appears when the entry becomes nonlinear or uses unsupported identifiers. Examples include x², x(x+2), or division by a variable expression. Rewrite the problem as a linear inequality, then solve it again.

8. Can I save my solved result?

Yes. After solving, use the CSV button for spreadsheet-style export or the PDF button for a portable report. Both options capture the displayed solution details so you can review or share them later.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.