Inequality Solver — Solve ax + b > c
Solution
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Steps
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Interval Notation
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How to Solve Linear Inequalities
A linear inequality is similar to a linear equation but uses inequality symbols (>, <, >=, <=) instead of an equals sign. To solve ax + b > c, follow the same steps as solving an equation: subtract b from both sides, then divide by a.
The critical rule is: when you multiply or divide both sides by a negative number, you must flip the inequality sign. For example, -2x > 6 becomes x < -3 (the > becomes <). This is the most common mistake students make.
The solution to an inequality is typically a range of values, expressed in interval notation. For example, x > 5 is written as (5, infinity), while x <= 3 is written as (-infinity, 3]. Round brackets mean the endpoint is excluded; square brackets mean it is included.
Frequently Asked Questions
Why does the inequality sign flip when dividing by a negative?
Multiplying or dividing by a negative reverses the order of numbers. For example, 2 < 3, but multiplying both sides by -1 gives -2 > -3. The sign must flip to maintain the truth of the statement.
What is interval notation?
Interval notation uses parentheses and brackets to describe a range. (a, b) means all numbers between a and b, not including a or b. [a, b] includes both endpoints. A parenthesis is always used next to infinity.
Can an inequality have no solution?
Yes. For example, 0x + 5 > 10 simplifies to 5 > 10, which is false. No value of x can make it true, so there is no solution (empty set).