Inequality Word Problems

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, or equal to the other. It uses symbols like >, <, ≥, and ≤.

The symbol '>' means 'greater than'. It indicates that the value on the left side of the inequality is larger than the value on the right side.

The symbol '<' means 'less than'. It indicates that the value on the left side of the inequality is smaller than the value on the right side.

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left side is either larger than or equal to the value on the right side.

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left side is either smaller than or equal to the value on the right side.

You can represent this situation with an inequality. For example, if a person has $25 and wants more than $150, it can be represented as $$25 + 0.50x > 150$$ , where x is the number of items sold.

The first step in solving an inequality is to isolate the variable on one side of the inequality sign, similar to solving an equation.

The solution of an inequality represents a range of values that satisfy the condition. For example, if the solution is $$x ≥ 12$$ , it means x can be 12 or any number greater than 12.

A real-world example is budgeting. If you want to spend no more than $50 on groceries, you can represent this as an inequality: $$x ≤ 50$$ , where x is the total amount spent.

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