Understanding Inequalities on a Number Line
An inequality describes a range of values, not always one value. A number line makes that range visible. It shows where the answer begins, where it ends, and whether an endpoint is included. This calculator uses those ideas to turn algebra into a clear diagram.
Why the Graph Matters
Students often solve the algebra correctly but draw the endpoint wrongly. An open circle means the boundary value is not part of the answer. A closed circle means the boundary value is included. A ray points toward every value that satisfies the statement. A segment shows a bounded compound solution.
How Linear Inequalities Are Solved
A linear inequality can look like ax + b < c. First, move the constant term. Then divide by the coefficient of x. The important rule appears when the coefficient is negative. Dividing by a negative number reverses the inequality sign. The calculator shows that step so the final direction is easier to check.
Direct and Compound Inputs
The direct mode is useful when the inequality is already isolated. For example, x ≥ 4 can be graphed immediately. The linear mode handles expressions like 3x − 6 < 12. The compound mode handles ranges such as −2 < x ≤ 5. These options cover many classroom and homework formats.
Interval and Set Notation
The result also appears in interval notation. Parentheses mean excluded endpoints. Brackets mean included endpoints. The same solution appears in set-builder notation for comparison. Seeing both formats helps connect graphing, algebra, and written answers.
Accuracy and Learning Value
The number line range can be adjusted for small or large values. Tick spacing helps create a neat display. Decimal precision controls rounded output. Export buttons save the result for worksheets, notes, or quick records. The example table gives ready test cases. Use it to compare open endpoints, closed endpoints, rays, segments, and all real solutions.
Common Mistakes to Avoid
Do not treat every endpoint the same way. Check the sign first. Then check the symbol. A strict symbol uses an open circle. An inclusive symbol uses a closed circle. For compound statements, read both sides. The solution must satisfy both conditions at once. A neat graph prevents many simple answer errors during every final review.