Inequalities (Lesson 2)

You’re back! Ready for some more math? Let’s go. I highly recommend you have some paper and a pencil, scrap paper will do!

Let’s start tackling inequalities. A repeat of the standard directions:

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.

By now these instructions are a little more familiar to you. The answer is A if A is greater, B if B is greater, C if they are equal, and D stands for don’t know!

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

y < 5      

Quantity A                          Quantity B

y                                              7

Which is greater, quantity A or quantity B? Just focus on what is written below Quantity A and Quantity B. What don’t we know?

We don’t know what y is worth. The beautiful thing about math is, unlike life, it gives you the answers you need! Like life, sometimes you need to work for them a little bit.

To figure out what y is worth, look at the question:

y < 5      

y is less than (<) or equal to (the line under the <) 5. y is less than or equal to 5.

What is the BIGGEST value y could have? Write that down:

Since y is less than or equal to 5, the biggest value it could have is 5.

What are some smaller values that y could be? Well, zero, for example. y could be worth zero, since zero is less than five. Let’s also pick a negative number, say -10. (-10 is less than 5; you’d much rather have $5 than have overdrawn your checking account by $10!)

Now we have three sample values for y. I recommend jotting them down next to y.

So what is greater, Quantity A or Quantity B? It’s Quantity B.

Ask yourself: What would have to happen for Quantity A and Quantity B to be equal? To be equal, y would need to be worth 7. Could y be worth 7? No, y is less than or equal to 5. It can’t get bigger than 5. We can be confident in our answer of B.

See you tomorrow!