24_25 Inequality Review

An inequality is a mathematical statement that compares two expressions and shows that one is less than, greater than, less than or equal to, or greater than or equal to the other.

The symbol '<' means 'less than'. For example, $$x < 5$$ means x is less than 5.

The symbol '>' means 'greater than'. For example, $$x > 3$$ means x is greater than 3.

Subtract 2 from both sides: $$\frac{1}{2}x < 1$$ . Then multiply both sides by 2: $$x < 2$$ .

Subtract 3 from both sides: $$15 < 3n$$ . Then divide by 3: $$5 < n$$ or $$n > 5$$ .

To graph an inequality, use a number line. Use an open circle for '<' or '>' and a closed circle for '≤' or '≥'. Shade the region that represents the solution.

This inequality represents the maximum number of miles (x) that can be driven in a car rental without exceeding a total cost of $95.

The symbol '≤' means 'less than or equal to'. For example, $$x ≤ 4$$ means x is less than or equal to 4.

The symbol '≥' means 'greater than or equal to'. For example, $$x ≥ 2$$ means x is greater than or equal to 2.

The solution of an inequality is represented by a shaded region on a number line, indicating all possible values that satisfy the inequality.