Inequalities & Number Lines

Reading inequality symbols

An inequality compares values that are not necessarily equal: < (less than), > (greater than), ≤ (at most), ≥ (at least). "At most 9" means x ≤ 9; "fewer than 5" means x < 5.

When you study reading inequality symbols, slow down and write one example in your notebook without looking at the screen. That active step is what turns reading into learning.

Solving and graphing

Solve an inequality the same way you solve an equation. Then graph the solution on a number line: an open circle for < or >, a closed (filled) circle for ≤ or ≥.

An equation says two expressions have the same value. Whatever you do to one side, you must do to the other to keep the balance.

Check your solution by substituting it back into the original equation. If both sides match, your answer is correct.

Why this matters

Inequalities & Number Lines shows up constantly in solve like equations, then graph every value that works. It also connects to what you will see on homework, quizzes, and the next unit in this grade.

Teachers often move fast in class. This page is here so you can pause, re-read, and practice until the idea feels familiar, not just until you have memorized a rule for one day.

Common mistakes to avoid

Rushing to the answer without writing steps. Middle-school math rewards clear work, and you catch errors earlier when steps are visible.

Mixing up similar ideas from the same topic. If two terms feel alike, make a two-column note: what is the same, what is different, and one example of each.

Key ideas from this lesson

1. Reading inequality symbols
2. Solving and graphing