# Inequality Verification

• October 20th 2009, 08:23 AM
ElectroNerd
Inequality Verification
Hey Everyone,

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

Thanks.
• October 20th 2009, 08:36 AM
Hello ElectroNerd
Quote:

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 $\geq$? And when a problem says "minimum number of..." wouldn't that be $<$? Just need to verify that (Wink).

Thanks.

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

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

• October 20th 2009, 08:48 AM
ElectroNerd
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 http://k12highschools.com/ec/pub/K12...pChar/8226.gif (3w)http://k12highschools.com/ec/pub/K12...pChar/8805.gif112

2w + 2 http://k12highschools.com/ec/pub/K12...pChar/8226.gif (3w) < 112

2w + 2 http://k12highschools.com/ec/pub/K12...pChar/8226.gif (3w) > 112

2w + 2 http://k12highschools.com/ec/pub/K12...pChar/8226.gif (3w)http://k12highschools.com/ec/pub/K12...pChar/8804.gif112

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

200whttp://k12highschools.com/ec/pub/K12...pChar/8805.gif4500 + 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?
• October 20th 2009, 08:51 AM
ElectroNerd
Quote:

Originally Posted by Grandad
Hello ElectroNerdNo, I think you have this the wrong way round. If the greatest possible value of $x$ is $a$, then $x \le a$.

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

Well I switch around the inequalites. So for the minimum number of something it would be $n\leq$ So it would still be right.