Inequalities (Lesson 3)

Let’s take it up a notch!

Official language for inequality problems:

Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the following four answer choices:

A.      Quantity A is greater.

B.      Quantity B is greater.

C.      The two quantities are equal.

D.      The relationship cannot be determined from the information given.

A symbol that appears more than once in a question has the same meaning throughout the question.

Question (I recommend copying this onto your scrap paper):

8y – 11 > 5          

Quantity A                          Quantity B

y                                              1

Which is greater, quantity A or quantity B? Once again we don’t know (yet!) what y is worth. To figure it out, we look at the question:

8y – 11 > 5          

We need to get y alone on one side. y is like that person you want to talk to at a party. Maybe you want to ask them out, maybe you want to find out where they got their great sneakers; either way, it’s easiest if they are alone and to the side of the crowd, right? So who is ruining the moment for us?

8y – 11 > 5          

Well, that 11 is to start. The 8 is as well, but it’s always easiest to handle any numbers that are being added or subtracted first, so we’ll start by handling the 11. Since 11 is being subtracted, we are going to add it to both sides. (Why both sides? The two sides of the inequality are like twins – if you give one a cookie, you better give the other one a cookie.)

 8y  > 16

Is y alone to one side yet? No, now the 8 is ruining the moment! Since 8 is being multiplied by y, we are going to divide both sides by 8.

y > 2        

y is greater than or equal to 2. Repeat to yourself: y is greater than or equal to 2. It may help to make a number line:

What is the biggest value y could have? Well, really really big!  It could be 1,000,000. It could be even bigger than that.

What is the smallest value y could have? 2.

Could it be 1? No, because 1 is less than 2, and y is greater than or equal to 2.

Could it be 10? Yes, because 10 is greater than 2.

If you remember, the original question was:

8y – 11 > 5          

Quantity A                          Quantity B

y                                              1

Now we have three sample values for y. Jot them down next to y.

So what is the answer from the choices below:

A.      Quantity A is greater.

B.      Quantity B is greater.

C.      The two quantities are equal.

D.      The relationship cannot be determined from the information given.

That’s right, it’s A! Quantity A is greater. y is greater than 1.

Good work today!