Linear Inequalities

Equations vs Inequalities

Equations use $=$. Inequalities use: $<$, $>$, $\leq$, $\geq$

Solving Inequalities

Solve them exactly like equations. Same steps, same logic.

But there’s one important difference…

The Flip Rule

When you multiply or divide by a negative number, you must flip the inequality sign.

$<$ becomes $>$, and $>$ becomes $<$

Why? Think about it: $2 > 1$

Multiply both sides by $-1$: $-2 \text{ ? } -1$

The answer is $-2 < -1$. The direction reversed.

Example

Solutions Are Different

• Equation: One answer ($x = 4$)
• Inequality: A range of answers ($x < 4$)

An inequality tells you all values that work, not just one.