Mastering Linear Inequalities: Understanding, Solving and Graphing Techniques

linear inequality

is similar to a linear equation, but the equal sign is replaced with an inequality symbol.

A linear inequality is a mathematical expression that compares two expressions using an inequality symbol like >, <, ≥, or ≤. An example of a linear inequality is 2x + 3 ≤ 7. In this inequality, x is a variable, and it symbolizes any number that satisfies the inequality. Solving a linear inequality involves finding the set of values of the variable that make the inequality true. You can solve a linear inequality using the same methods as you would use to solve a linear equation. However, when you multiply or divide both sides of an inequality by a negative number, you must reverse the direction of the inequality. For example, to solve the inequality 2x + 3 ≤ 7, you can subtract 3 from both sides of the inequality to get 2x ≤ 4. Then, you can divide both sides by 2 to obtain x ≤ 2. Therefore, any number less than or equal to 2 satisfies the inequality. Graphically, a linear inequality represents a region on a coordinate plane bounded by a line. If the inequality is strict (< or >), the line is drawn as a dashed line. The region that satisfies the inequality is shaded either above or below the line. If the inequality includes equality (≤ or ≥), the line is drawn as a solid line and the region that satisfies the inequality is shaded on or above the line or on or below the line.

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