Algebra / Linear Inequalities
Linear Inequalities
Linear inequalities use symbols such as $<$, $>$, $\le$, and $\ge$ to describe ranges of values. Solving them is similar to solving linear equations, except the inequality symbol reverses when both sides are multiplied or divided by a negative number.
Least you need to know
- Multiplying or dividing both sides of an inequality by a negative number reverses the inequality symbol.
- A two-variable linear inequality describes a half-plane whose boundary is a line.
Key notation
- $x<5$ — All values of $x$ less than 5
Worked example
- Isolate the variable.
- Reverse the inequality only when multiplying or dividing by a negative number.
Common mistakes
- Strict inequalities do not include equality.
- Boundary values depend on the inequality symbol.
How to recognize it
- The problem uses $<$, $>$, $\le$, or $\ge$.
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