What is the answer to: a+4 ≥ 2a?

**What is the answer to:**

a+4 ≥ 2a

It asks you to isolate the variable.

My answer booklet says 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**. My answer book does not explain it.

Please Help!

Your help is greatly appreciated!!

Re: What is the answer to: a+4 ≥ 2a?

Quote:

Originally Posted by

**gredude** **What is the answer to:**

a+4 ≥ 2a

It asks you to isolate the variable.

My answer booklet says 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**. My answer book does not explain it.

Please Help!

Your help is greatly appreciated!!

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

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.

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.

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!

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??

Re: What is the answer to: a+4 ≥ 2a?

Wait a second, is **4 ≥ a** the same thing as saying **4 ≥ 1a**. By subtracting **a**from **2a**, you are left with **1a** or just **a**?

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

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 **a**from **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