Algebra Strategy Guide 3rd Edition Page 83 Question 12

[yrasheed18]

On page 83, question 12 of the GRE Algebra strategy guide 3rd edition, it says

a+4 ≥ 2a

It asks you to isolate the variable.

The answer on page 93 says that the correct answer is
4 ≥ a.

I do not know how they reached this conclusion. My thought process told me to divide a+4 by a and then divide 2a by a. That left me with 4≥2.

What am I doing wrong? How do i get the correct answer of
4 ≥ a. The book does not explain it.

Please Help!
Your help is greatly appreciated!!

[tommywallach]

Hey Rasheed,

This is a common error when you aren't practiced up enough on algebra. That being said, I'd recommend you re-read the chapters on basic manipulation. You've made two errors in your assessment:

What is (a + 4) / a ?

You seem to think it's just 4. However, it isn't. You have to divide both a and 4 by a

(a + 4) / a = a/a + 4/a = 1 + 4/a

If you want to get rid of the a, you should simply subtract a from both sides of the equation:

a+4 ≥ 2a

subtract a from both sides:

4 ≥ a

Don't always jump to multiplication/division when manipulating equations/inequalities. Remember that addition and subtraction are much simpler and easier!

-t