Solving and Graphing Inequalities
Solve and graph inequalities in Grade 10 algebra. Apply inverse operations to isolate variables, reverse inequality signs when dividing by negatives, and shade solution regions on number lines.
Key Concepts
New Concept An inequality is a mathematical statement comparing quantities that are not equal. There are four inequality symbols: $<, , \leq, \geq$.
What’s next Next, you’ll master the rules for solving these inequalities and learn how to graph their solutions on a number line.
Common Questions
How do you solve a linear inequality?
Use the same inverse operations as solving equations. The key difference: when you multiply or divide both sides by a negative number, reverse the inequality sign.
How do you graph the solution of a linear inequality on a number line?
Find the boundary point (solve the related equation). Use an open circle for strict inequalities (< or >) and closed circle for ≥ or ≤. Shade the region that satisfies the inequality.
What real-world situations use inequalities?
Height requirements, speed limits, minimum age requirements, and budget constraints all use inequalities. Any situation with at least, at most, no more than, or no less than involves inequality reasoning.