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simplify expression 8 + 5(x + 3) - 2x: I get 14x
- Thread starter mercedez
- Start date
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).
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).
D
Deleted member 4993
Guest
Re: simplify expression
You need to review polynomial and simplification. Review at:
http://www.purplemath.com/modules/polyadd.htm
work through the example problems - carefully.
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.
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.
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.