One Step Inequalities Calculator

Solve simple inequalities with guided steps and checks. Choose operations, signs, and decimal rounding choices. Download clean reports for class, tutoring, or practice today.

Calculator Form

Example Data Table

Type Original Inequality Operation Used Solution Interval
Addition x + 5 < 12 Subtract 5 x < 7 (-∞, 7)
Subtraction x - 9 ≥ 3 Add 9 x ≥ 12 [12, ∞)
Multiplication -4x ≤ 20 Divide by -4 x ≥ -5 [-5, ∞)
Division x / -2 > 6 Multiply by -2 x < -12 (-∞, -12)

Formula Used

Addition: x + a < b becomes x < b - a.

Subtraction: x - a < b becomes x < b + a.

Multiplication: ax < b becomes x < b / a when a is positive.

Division: x / a < b becomes x < b × a when a is positive.

When multiplying or dividing both sides by a negative number, reverse the inequality sign.

How to Use This Calculator

  1. Enter the variable name, such as x, y, or n.
  2. Select the one step inequality type.
  3. Enter the value of a and the right side value b.
  4. Choose the inequality sign.
  5. Set decimal places for rounded output.
  6. Add an optional test value to check the solution.
  7. Press calculate to view steps, interval notation, and graph guidance.
  8. Use the CSV or PDF button to save the answer.

Understanding One Step Inequalities

One step inequalities are simple statements that compare two quantities. They use symbols such as less than, greater than, less than or equal to, and greater than or equal to. The goal is to isolate the variable with one inverse operation. This makes them a strong first topic for algebra practice.

Why the Method Works

An inequality stays balanced when the same allowed operation is applied to both sides. Addition and subtraction move constants away from the variable. Multiplication and division remove a coefficient. The main rule is easy to miss. Reverse the inequality symbol when multiplying or dividing by a negative number.

Reading the Answer

The answer can be written as an inequality, interval notation, or a number line statement. For x < 4, all values smaller than four work. The interval is (-∞, 4). A number line uses an open point at four. Then it shades left. For x ≥ 4, the point is closed. The shading moves right.

Using Checks

A test value helps confirm the result. Choose a number from the shaded region. Substitute it into the original inequality. If the statement is true, the solution direction is likely correct. If it is false, check the inverse operation and sign change.

Common Mistakes

Many errors come from rushing. Students may subtract when they should add. They may divide by a negative coefficient without flipping the sign. Decimal rounding can also hide exact results. Keep extra decimal places when answers are used in later work. Write each step clearly before graphing the result.

When This Calculator Helps

This calculator supports practice, homework checking, tutoring, and quick review. It explains the operation used, shows the final inequality, builds interval notation, and describes the number line. It also gives export options, so the result can be saved for notes or shared with a teacher.

FAQs

What is a one step inequality?

It is an inequality solved with one inverse operation. Examples include x + 3 < 9, x - 5 ≥ 2, 4x ≤ 20, and x / 3 > 7.

When do I flip the inequality sign?

Flip the sign only when multiplying or dividing both sides by a negative number. Do not flip it for addition or subtraction.

Can this calculator handle decimals?

Yes. You can enter decimal values for the constant, coefficient, right side, and optional test value. You can also choose the rounding level.

What does interval notation mean?

Interval notation describes all possible answers as a range. Parentheses exclude an endpoint. Brackets include an endpoint. Infinity always uses parentheses.

Why is my endpoint open?

The endpoint is open when the sign is less than or greater than. Those signs do not include the boundary value.

Why is my endpoint closed?

The endpoint is closed when the sign includes equal to. That means less than or equal to, or greater than or equal to.

What is a test value?

A test value is a number you substitute into the original inequality. It checks whether that number belongs to the solution set.

Can I download my result?

Yes. After calculation, use the CSV button for spreadsheet data. Use the PDF button for a simple printable report.

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