What does this calculator convert?

This calculator converts a one-variable linear inequality into interval notation. For example, x > 3 becomes (3, ∞), while x ≤ -2 becomes (-∞, -2].

The page is intentionally focused on one search task: turning an inequality into interval notation. The broader interval notation calculator covers the general bidirectional idea, but this page opens directly on the inequality-to-interval direction.

What does inequality to interval notation mean?

Converting an inequality to interval notation means writing all values that satisfy the inequality as an interval using parentheses, brackets, and infinity symbols.

For example, x < 5 describes all real numbers less than 5. In interval notation, that solution set is (-∞, 5). The number 5 is not included, so the endpoint uses a parenthesis.

The inequality x ≥ 1 includes 1 and every number greater than 1. Its interval notation is [1, ∞), with a bracket at 1 because 1 belongs to the solution set.

How do you choose parentheses or brackets?

Parentheses or brackets are chosen according to whether the boundary value is included in the solution. Strict inequalities exclude the boundary; inequalities with equality include it.

• x < a or x > a: the boundary is not included, so use a parenthesis.
• x ≤ a or x ≥ a: the boundary is included, so use a bracket.
• Infinity and negative infinity always use parentheses because they are not actual endpoint values.
• Intervals are written from left to right, from the smaller side to the larger side.

How is a linear inequality isolated?

A linear inequality is isolated by moving terms until x is alone, then converting the final inequality into interval notation. If you multiply or divide by a negative number, the inequality direction must reverse.

1. Move variable terms to one side and constant terms to the other side.
2. Simplify both sides.
3. Divide by the coefficient of x.
4. Reverse the inequality direction if the coefficient you divide by is negative.
5. Convert the isolated inequality into interval notation.

Example: converting 2x - 4 < 6

The inequality 2x - 4 < 6 simplifies to x < 5, so the interval notation is (-∞, 5).

1. 2x - 4 < 6
2. 2x < 10
3. x < 5
4. 5 is not included because the sign is <.
5. Interval notation: (-∞, 5)

This result includes every real number less than 5, but not 5 itself. That is why the endpoint at 5 is open.

Example: why does -3x + 6 ≥ 12 change direction?

The inequality -3x + 6 ≥ 12 changes direction because isolating x requires division by a negative number. The result is x ≤ -2, which becomes (-∞, -2].

1. -3x + 6 ≥ 12
2. -3x ≥ 6
3. Divide both sides by -3.
4. Because the divisor is negative, ≥ becomes ≤.
5. x ≤ -2
6. Interval notation: (-∞, -2]

How is this page different from the general interval notation calculator?

This page is a narrower landing page for users who specifically want to convert an inequality into interval notation. The general interval notation calculator is broader and can explain the notation from more than one direction.

The runtime is shared, but the content and page intent are different. Here the first job is solving a linear inequality and writing the answer as an interval.

• This page: start with an inequality, get interval notation.
• General interval notation: compare interval notation and related forms more broadly.
• Number line inequality: focus on the visual number-line representation.

Which inequalities are outside this page's scope?

This calculator is intended for linear inequality to interval notation conversion. Absolute value, quadratic, two-variable, rational, or compound inequalities may need different tools or a longer solution process.

• Absolute value inequalities such as |x - 2| < 5 are not the main scope here.
• Quadratic inequalities such as x² - 4 > 0 require sign intervals or a parabola-based method.
• Compound inequalities such as 2 < x ≤ 7 require a different interval-building pattern.
• Two-variable inequalities such as y < 2x + 1 need a plane-region graph.
• Intersections or unions of multiple inequalities require set operations.

How do you read interval notation after conversion?

After conversion, read the interval by checking the boundary value first and then the endpoint symbol. The symbol tells you whether the boundary belongs to the solution set.

• (2, ∞): all numbers greater than 2, not including 2.
• [2, ∞): all numbers greater than or equal to 2, including 2.
• (-∞, 4): all numbers less than 4, not including 4.
• (-∞, 4]: all numbers less than or equal to 4, including 4.

A good check is to translate the interval back into words. If [2, ∞) reads as “x is at least 2,” the conversion is internally consistent.

Common mistakes

Most mistakes in inequality-to-interval conversion come from endpoint symbols, sign direction, and the use of infinity.

• Using the same endpoint symbol for < and ≤.
• Forgetting to reverse the inequality after dividing by a negative number.
• Putting a bracket next to infinity.
• Writing the interval in the wrong left-to-right order.
• Turning x > a into (-∞, a) instead of (a, ∞).
• Trying to use a linear tool for a non-linear inequality.

Limitations of this calculator

This calculator is a focused tool for converting one linear inequality into interval notation. It is not a computer algebra system and does not solve every possible inequality type.

The result depends on the entered inequality being a supported linear inequality. Quadratic, absolute value, rational, trigonometric, two-variable, or compound inequalities may require a different solver or a different explanation.