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 ≤.

You can represent this situation with an inequality. For example, if a person earns $15 per hour and wants to earn at least $105, the inequality would be $$15h \, \ge \, 105$$ .

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left can be less than or equal to the value on the right.

To set up an inequality for a budget constraint, add the costs of items and set it less than or equal to the total budget. For example, if you have $8.50 to spend and a binder costs $6.89, the inequality for pens (x) would be $$6.89 + 0.59x \le 8.50$$ .

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 $$x \le 12$$ , it means x can be any number less than or equal to 12.

An inequality has no solution if there are no values that can satisfy the condition. For example, $$x > 12$$ and $$x \le 12$$ cannot be true at the same time.

To check if a value satisfies an inequality, substitute the value into the inequality and see if the statement is true.

A real-world example of using inequalities is budgeting. If you have a maximum amount to spend, you can set up an inequality to determine how much you can spend on different items.

This inequality represents the maximum speed Katie can increase her speed without exceeding the speed limit of 45 mph, starting from 30 mph.