Inequality Word Problems

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

The symbol '>' means 'greater than'. For example, $$x > 5$$ means x is greater than 5.

The symbol '<' means 'less than'. For example, $$x < 3$$ means x is less than 3.

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

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

To solve a simple inequality, isolate the variable on one side of the inequality sign using inverse operations, similar to solving an equation.

Subtract 3 from both sides to get $$2x < 8$$ .

Add 5 to both sides to get $$x ≥ 15$$ .

To graph an inequality, use an open circle for '<' or '>' and a closed circle for '≤' or '≥'. Shade the region that satisfies the inequality.

A compound inequality combines two inequalities, often using 'and' or 'or'. For example, $$3 < x < 7$$ means x is greater than 3 and less than 7.