# What is the answer to: a+4 ≥ 2a?

• Feb 19th 2013, 02:39 PM
gredude
What is the answer to: a+4 ≥ 2a?

a+4 ≥ 2a

It asks you to isolate the variable.

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. My answer book does not explain it.

• Feb 19th 2013, 02:46 PM
topsquark
Re: What is the answer to: a+4 ≥ 2a?
Quote:

Originally Posted by gredude

a+4 ≥ 2a

It asks you to isolate the variable.

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. My answer book does not explain it.

Your problem boils down to order of operations.
$\displaystyle \frac{a + 4}{a} \neq 4$

In fact
$\displaystyle \frac{a + 4}{a} = 1 + \frac{4}{a}$

We divide each term by a, not just the first one.

The solution:
$\displaystyle a + 4 \geq 2a$

$\displaystyle a + 4 - a \geq 2a - a$

Can you take it from here?

-Dan
• Feb 19th 2013, 03:50 PM
gredude
Re: What is the answer to: a+4 ≥ 2a?
Quote:

Originally Posted by topsquark
Your problem boils down to order of operations.
$\displaystyle \frac{a + 4}{a} \neq 4$

In fact
$\displaystyle \frac{a + 4}{a} = 1 + \frac{4}{a}$

We divide each term by a, not just the first one.

The solution:
$\displaystyle a + 4 \geq 2a$

$\displaystyle a + 4 - a \geq 2a - a$

Can you take it from here?

-Dan

Im sorry, but I still don't understand. Why are you subtracting a from 2a?

Wouldnt that leave you with the number 2? I am not sure how you reached you answer. Could you give me a simpler explanation. I really appreciate it.
• Feb 19th 2013, 04:44 PM
HallsofIvy
Re: What is the answer to: a+4 ≥ 2a?
I hope that the "gre" in "gredude" doesn't stand for "graduate record exam"! You are misundertanding things that are covered in a class for 12 to 13 year old students- and that follow directly from more basic arithmetic. No, "2a- a" is NOT 2. Subtracting a does not mean "erase the a". If you have two elephants and "take away" one elephant, you have left one elephant, not the number "2". If a= 5, 2a= 10 and 2a- a is 10- 5= 5= a.
• Feb 19th 2013, 05:10 PM
gredude
Re: What is the answer to: a+4 ≥ 2a?
I'm sorry, i don't understand. Please could you just go over the problem step by step. Im sorry, but I really need help!
• Feb 19th 2013, 05:12 PM
gredude
Re: What is the answer to: a+4 ≥ 2a?
This is as far as I can understand.

You are subtracting a from a+4. Which leaves you with 4. am I right so far??
• Feb 19th 2013, 05:18 PM
gredude
Re: What is the answer to: a+4 ≥ 2a?
Wait a second, is 4 ≥ a the same thing as saying 4 ≥ 1a. By subtracting afrom 2a, you are left with 1a or just a?

So basically you subtracted a from both sides to get the answer... Is that correct?
• Feb 23rd 2013, 07:18 AM
topsquark
Re: What is the answer to: a+4 ≥ 2a?
Quote:

Originally Posted by gredude
Wait a second, is 4 ≥ a the same thing as saying 4 ≥ 1a. By subtracting afrom 2a, you are left with 1a or just a?

So basically you subtracted a from both sides to get the answer... Is that correct?

That is correct. Also, 1a = a.

-Dan