1. ## Inequality Verification

Hey Everyone,

I just want to make sure I understand this... When a problem says "greatest possible value" wouldn't they mean $\displaystyle \geq$? And when a problem says "minimum number of..." wouldn't that be $\displaystyle <$? Just need to verify that .

Thanks.

2. Hello ElectroNerd
Originally Posted by ElectroNerd
Hey Everyone,

I just want to make sure I understand this... When a problem says "greatest possible value" wouldn't they mean $\displaystyle \geq$? And when a problem says "minimum number of..." wouldn't that be $\displaystyle <$? Just need to verify that .

Thanks.
No, I think you have this the wrong way round. If the greatest possible value of $\displaystyle x$ is $\displaystyle a$, then $\displaystyle x \le a$.

And if the minimum number of something is $\displaystyle n$, then the actual number is $\displaystyle \ge n$.

3. Here are my problems:

1. The length of a rectangle is three times its width. If the perimeter is at most 112 centimeters, what is the greatest possible value for the width? Write an inequality to model the problem.

2w + 2 (3w)112

2w + 2 (3w) < 112

2w + 2 (3w) > 112

2w + 2 (3w)112

And:

2. Josephine started a business selling cosmetics. She spent $4500 to obtain her merchandise, and it costs her$200 per week for general expenses. She earned $550 per week in sales. What is the minimum number of weeks it will take for Josephine to make a profit? Write an inequality to model the problem. 550w > 4500 + 200w 200w > 4500 + 550w 550w < 4500 + 200w 200w4500 + 550w So for the first problem I think it's the first answer and for the second problem I think it's the third answer. Am I correct? 4. Originally Posted by Grandad Hello ElectroNerdNo, I think you have this the wrong way round. If the greatest possible value of$\displaystyle x$is$\displaystyle a$, then$\displaystyle x \le a$. And if the minimum number of something is$\displaystyle n$, then the actual number is$\displaystyle \ge n$. Grandad Well I switch around the inequalites. So for the minimum number of something it would be$\displaystyle n\leq\$ So it would still be right.