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Solve linear inequalities step-by-step with number line visualization and interval notation
An inequality calculator is a powerful tool that helps solve linear inequalities involving variables. Unlike equations that show equality, inequalities show relationships where one side is less than, greater than, less than or equal to, or greater than or equal to the other side.
One of the most important rules when solving inequalities is the flip rule: when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol. For example, if you have -2x < 6 and divide both sides by -2, the inequality becomes x > -3.
Interval notation is a concise way to represent solution sets. Parentheses ( ) indicate that an endpoint is not included (open circle), while brackets [ ] indicate that an endpoint is included (closed circle). Infinity symbols always use parentheses.
You flip the inequality sign when you multiply or divide both sides by a negative number. This is because multiplying or dividing by a negative reverses the order of numbers on the number line.
An open circle indicates that the endpoint is not included in the solution (< or >), while a closed circle indicates that the endpoint is included (≤ or ≥).
Use parentheses ( ) for endpoints that are not included and brackets [ ] for endpoints that are included. For example, x < 5 is written as (-∞, 5), and x ≥ 3 is written as [3, ∞).
Yes, some inequalities have no solution. For example, if you simplify an inequality and get a false statement like 5 < 2, the inequality has no solution.
When an inequality simplifies to a true statement like 3 < 5, it means the original inequality is true for all values of the variable, so the solution is all real numbers, written as (-∞, ∞).
First, move all variable terms to one side and all constant terms to the other side. Then isolate the variable by using inverse operations, remembering to flip the inequality sign if you multiply or divide by a negative number.
Compound inequalities involve two separate inequalities joined by "and" or "or". For example, 3 < x < 7 means x is greater than 3 AND less than 7.
A number line provides a visual representation of the solution set, making it easier to understand which values satisfy the inequality. It shows the range of solutions and whether endpoints are included.
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