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, $$x ≥ 10$$ means x is greater than or equal to 10.

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

You can represent this situation using an inequality. For example, if someone wants to spend less than $15, you can write $$x < 15$$ .

Identify the total amount available and the costs involved. For example, if you have $15 to spend on pizza slices at $2.50 each and a soda at $1.75, the inequality would be $$15 > 2.50x + 1.75$$ .

The first step is to isolate the variable on one side of the inequality. This often involves adding, subtracting, multiplying, or dividing both sides by the same number.

When you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign.

You can check by substituting the solution back into the original inequality to see if it holds true.