simplify expression 8 + 5(x + 3) - 2x: I get 14x

mercedez

New member
Joined
Nov 13, 2008
Messages
1
8+5(x+3)-2x

My answer
13x+3-2x
16x-2x
14x

I know this is incorrect it gives me options and my answer is not one of the options. What am i doing wrong?
 

Loren

Senior Member
Joined
Aug 28, 2007
Messages
1,299
Re: simplify expression

You are not showing each step so we can't tell what you are doing wrong. Please start with 8+5(x+3)-2x and show each individual step so we can identify what you are doing wrong.
 

chivox

Junior Member
Joined
Nov 13, 2008
Messages
119
Re: simplify expression

The mistake you're making is clear from the work shown: You did not perform the "order of operations" correctly. With arithmetic expressions like this, there is a specific order in which you have to do each step. You did the steps in the wrong order. Take a look at this Web site, prepared by an organization to help students prepare for the New York Regents exam:

http://regentsprep.org/Regents/math/orderop/Lorder.htm

Now, take a look at your problem:

8+5(x+3)-2x

Your work shows that you added 8+5 to get 13. That was incorrect. If you remembered the PEMDAS (see the above Web site again if you have forgotten), you know that you have to do "P"arentheses first. Therefore, the first step in simplifying this expression would be to take what is inside the parentheses and do that first. However, that is already in simplest terms. Next in PEMDAS is exponents. There aren't any of those in your problem, so we move on. The "M" in PEMDAS stands for "M"ultiplication, which, together with division left to right, is the next step. We have some multiplying to do:

5 is written next to the quantity (x+3), which indicates a multiplication.

Apply the distributive property:

5 (x+3) simplifies to 5x + 15.

Rewrite the whole expression, substituting "5x + 15" for "5 (x+3)":

8 + 5x + 15 - 2x

Next in PEMDAS is addition and subtraction, done at the same time, working left to right. In our expression, this really involves combining like terms. Can you take it from here?

There is an additional error in your work, in that combining like terms means getting a total for each term that has an "x" and each term that doesn't. Your work shows that you combined "13x + 3" to get "16x". That is a mistake, because the "3" doesn't have an "x" on it. You can only combine terms like this that are the same: terms with an x (just one x) can only be combined with other terms that have an x (just one of them), and terms without an x (just numbers) can only be combined with other terms without an x (just numbers).
 

Subhotosh Khan

Super Moderator
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Jun 18, 2007
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18,149
Re: simplify expression

mercedez said:
8+5(x+3)-2x

My answer
13x+3-2x <<< how did you get 13x? you cannot just add 8 and 5x to get 13x
16x-2x
14x

I know this is incorrect it gives me options and my answer is not one of the options. What am i doing wrong?
You need to review polynomial and simplification. Review at:

http://www.purplemath.com/modules/polyadd.htm

work through the example problems - carefully.
 

Bill51

New member
Joined
Nov 14, 2008
Messages
10
Mercedez:

There is a SEQUENCE in which you need to perform the simplification.

If I add some extra parentheses (), I think it may show you how to simplify.

I can change your expression to (8) + (5(x+3)) - (2x) without changing its value.

Now, working with this, apply this rule: ELIMINATE INNER PARENTHESES FIRST.

SO: (8) + (5x + 15) - (2x)

8 + 5x +15 - 2x

3x + 23.

So, with expressions like this, do the multiplying (or dividing) FIRST, then do the adding and subtracting.
 
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