Q: What is a compound inequality?

A compound inequality links two separate inequalities together, usually using the words 'AND' or 'OR'. An example is `3 < x < 10`. This calculator solves single linear statements, not compound chains.

Q: Does order of operations still apply?

Yes, standard PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) rules apply perfectly to inequalities just like they do to strict equals signs. You must combine like-terms first.

Question 1

What is a Linear Inequality?

Accepted Answer

An inequality compares two values or expressions, showing if one is less than, greater than, or simply not equal to another. A linear inequality means the variable (like 'x') has no exponents or roots (it is strictly to the first power).

Question 2

When do you flip the inequality sign?

Accepted Answer

The golden rule of inequalities: Whenever you multiply or divide both sides of an inequality by a negative number, you MUST flip the inequality sign to keep the statement mathematically true. (e.g., `<` becomes `>`, `≥` becomes `≤`). This calculator automatically handles this rule for you.

Question 3

What is Interval Notation?

Accepted Answer

Interval notation is a simplified way to write subsets of the real number line. It uses brackets `[ ]` to include a number (solid line/dot) and parentheses `( )` to exclude a number (open circle or infinity). For example, `x ≥ 5` is written as `[5, ∞)`.

Question 4

What does the 'AC' button do?

Accepted Answer

The 'AC' (All Clear) button instantly wipes your current equation, allowing you to quickly input a new math problem without needing to hold backspace.

Question 5

Does this calculator solve quadratic inequalities?

Accepted Answer

Currently, this specific tool is optimized strictly for Linear inequalities (equations without exponents like x²). If you enter complex parenthetical or quadratic structures, the calculator will return a format error.

Question 6

What does an open circle vs a closed circle mean on a graph?

Accepted Answer

When visualizing an inequality on a real number line, an open circle means the boundary number is NOT included (`<` or `>`). A closed, solid circle means the boundary number IS physically included as a valid answer (`≤` or `≥`).

Question 7

Is negative infinity written with a bracket or parenthesis?

Accepted Answer

Infinity (both positive and negative) is always written with a soft parenthesis `( )` in interval notation. Because infinity is a concept and not a reachable physical number, it is impossible to draw a 'hard bracket' bounding it.

Question 8

Can an inequality have 'no solution'?

Accepted Answer

Yes. In algebraic systems, you might get a result like `5 < 2`. Because 5 is fundamentally never less than 2, the statement is completely false, meaning there are zero valid values for variable `x`. This is called a 'no solution' or empty set.

Question 9

What is a compound inequality?

Accepted Answer

A compound inequality links two separate inequalities together, usually using the words 'AND' or 'OR'. An example is `3 < x < 10`. This calculator solves single linear statements, not compound chains.

Question 10

Does order of operations still apply?

Accepted Answer

Yes, standard PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) rules apply perfectly to inequalities just like they do to strict equals signs. You must combine like-terms first.

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Inequality Calculator

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