Inequalities Practice

Solving and graphing inequalities

Inequalities are mathematical statements that compare two expressions using symbols like >, <, ≥, and ≤. Unlike equations, which have exact solutions, inequalities describe ranges of values that satisfy a condition. They are essential in optimization, budgeting, and any situation involving limits or constraints.

Types of Inequalities

• One-step: Solve by performing a single operation (e.g., x + 3 > 7)
• Two-step: Require two operations to isolate the variable
• Compound: Two inequalities joined by "and" or "or"
• Absolute value: Inequalities involving |x| expressions

Critical Rule

When you multiply or divide both sides of an inequality by a negative number, you must flip the inequality sign. This is the most common mistake students make and the most important rule to remember. For example, if -2x > 6, dividing both sides by -2 gives x < -3 (the sign flips).

Graphing Inequalities

Inequalities are represented on number lines using open circles (for > and <) or closed circles (for ≥ and ≤), with arrows showing the range of valid values. On coordinate planes, linear inequalities create shaded half-planes separated by boundary lines.

Coming Soon

We are building an interactive inequalities engine with number line visualization, automatic sign-flip detection, and compound inequality support. Stay tuned for launch.