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PEMDAS and Parenthesis

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by ntquigley » Sat Oct 24, 2015 9:09 am
Question: When can parenthesis "go away"?

For example:
(x+15)+(3x-5)=180

The solution is to remove the parenthesis, and solve this:
x+15+3x-5=180

Obviously that is easy to solve. My question is WHY. How do I know when the parenthesis can disappear and when they cannot?

Here is the simple sample question: https://www.gmatprepnow.com/module/gmat- ... /video/859
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by Brent@GMATPrepNow » Sat Oct 24, 2015 9:21 am
Here's a free video that might help - https://www.gmatprepnow.com/module/gmat- ... /video/949

NOTE: The part you're interested in starts around 4:00

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Brent
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by [email protected] » Sat Oct 24, 2015 11:24 am
Hi ntquigley,

One of the standard rules in arithmetic is that you can combine LIKE terms.

When dealing with parentheses, there's often an 'interim' step that you have to go through BEFORE you combine terms.

As an example, I'm going to use your equation and modify it a bit...

(X+15) + 2(3X-5)=180

Notice how the second parenthesis is multiplied by 2. THAT math needs to be done before the like terms are combined...

X + 15 + 6X - 10 = 180

NOW, you can combine like terms:

7X + 5 = 180
7X = 175
X = 25

If you're dealing with parentheses in which you have like terms and no additional 'steps', then you can remove the parenthesis and combine the terms.

GMAT assassins aren't born, they're made,
Rich
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