Inequality Word Problems Test Review

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 or equal to'. It indicates that the value on the left is either greater than or equal to the value on the right.

You can represent this situation using an inequality, such as $$x + b ≥ c$$ , where $$x$$ is the amount earned, $$b$$ is any initial amount, and $$c$$ is the target amount.

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

To solve $$5x + 10 ≥ 100$$ , subtract 10 from both sides to get $$5x ≥ 90$$ , then divide both sides by 5 to find $$x ≥ 18$$ .

It represents that the variable $$x$$ must be greater than 18, indicating the minimum requirement needed to satisfy the condition.

This inequality means that the total earnings from driving $$x$$ miles at a rate of $0.85 per mile, plus a fixed fee of $375, must be greater than $450.

This inequality indicates that the total amount of money Stacy has, which is $25 plus $0.50 for each lemonade sold (represented by $$x$$ ), must be at least $150.

The constant term in an inequality represents a fixed value that can affect the overall outcome, such as initial amounts or fees.

To graph an inequality on a number line, use an open circle for 'greater than' or 'less than' and a closed circle for 'greater than or equal to' or 'less than or equal to', then shade the appropriate direction.