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.

'At most' indicates a maximum limit. For example, if a person can spend at most $8, it means they can spend $8 or less.

You can represent this with an inequality. For example, if someone wants to spend less than $10, it can be written as $$x < 10$$ .

The inequality is $$80 + 8x \, \ge \, 176$$ , where $$x$$ is the number of video games sold.

To solve an inequality, isolate the variable on one side using inverse operations, similar to solving an equation, while maintaining the direction of the inequality.

'At least' indicates a minimum limit. For example, if someone needs at least 100 signatures, it means they need 100 or more.

You can express this with an inequality. For example, if someone has $25 and sells lemonade for $0.50 each, the total can be represented as $$25 + 0.50x \, \ge \, 150$$ .

The first step is to identify the variables and what they represent in the context of the problem.

You can represent this with an inequality. For example, if someone has 520 signatures and needs at least 1000, with 6 weeks to collect more, it can be written as $$520 + 6x \, \ge \, 1000$$ .

The solution indicates that the variable $$x$$ can take any value that is 12 or greater.