4.2: Solving Inequality Word Problems

Front

What is an inequality?

Back

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.

Front

What does the symbol '≤' mean?

Back

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.

Front

How do you represent a situation where a person can speed up but not exceed a certain limit?

Back

You can represent this situation with an inequality, such as s ≤ limit, where 's' is the amount of speed increase.

Front

If a person caught at least three times as many fish this year than last year, how would you express this mathematically?

Back

You would express this as y ≥ 1/3 * current catch, where 'y' is the number of fish caught last year.

Front

What is the first step in solving an inequality word problem?

Back

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

Front

How do you solve the inequality s ≤ 15?

Back

To solve s ≤ 15, you determine that 's' can take any value up to and including 15.

Front

What does the inequality y ≥ 21 represent in the context of Todd's fish catch?

Back

It represents that Todd caught at least 21 fish last year.

Front

How do you set up an inequality for profit problems?

Back

You set up an inequality by expressing the profit as a product of the number of items sold and the profit per item, then comparing it to the desired profit.

Front

If a store wants to make a profit of no less than $5225 and makes $5.50 per bag, how do you express this as an inequality?

Back

You express this as 5.50x ≥ 5225, where 'x' is the number of bags sold.

Front

What is the solution to the inequality 5.50x ≥ 5225?

Back

The solution is x ≥ 950, meaning the store needs to sell at least 950 bags.