Solving linear inequalities
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A linear inequality is similar to a linear equation but uses inequality symbols like < or > instead of =. A solution to a linear inequality is any coordinate pair that makes the inequality true. A linear inequality describes a half-plane region on a coordinate plane where all points in the region satisfy the inequality, with the boundary line given by the related equation. To graph a linear inequality, you solve it for y, graph the boundary line as solid or dotted, and shade the correct half-plane above or below the line.
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Solving linear inequalities
- 2. Let’s Review A linear inequality is similar to a linear equation, but the equation sign is replaced with an inequality symbol. y = 3x + 12 y < 3x + 12
- 3. Let’s Review A solution of a linear inequality is any order pair that makes the inequality true.
- 4. Let’s Review A inequality described a region of a coordinate plane called a half-plane. All points in the region are solutions of the linear inequality. The boundary line of the region is the graph of the related equation.
- 5. Let’s Review Step 1: Solve the inequality for y. Step 2: Graph the boundary line. Use a solid line for < or > symbols. Use the dotted/ dashed line for > or < symbols. Step 3: Shade the half-plane above the line for y > or >. Shade the half-plane below the line for y< or <. Check your answer! Graphing a Linear Inequalities