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Question 214793: Hi, I am stumped with this problem, I asked my teacher to explain and went home to try and I am still unable to solve it. Can someone please help me and explain a step-by-step what I did wrong?
My problem is:
11-(X+5)=2[2(X-1)+7]
This is how I went about it.
11-(X+5)=2[2(X-1)+7]
11-X-5=2[2X-2+7]
10X-5=4X-4+14
10X-5=4X+10
10X-4X-5=10
6X-5=10
6X=10+5
6X=15
(1/6)(6/1)X=(1/6)(15/1)
X=5/2
The book says the answer should be
-4/5
Please help!!!
Thank you,
Trish
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! This is how I went about it.
11-(X+5)=2[2(X-1)+7]
11-X-5=2[2X-2+7]
10X-5=4X-4+14
This last step is where you went wrong. 11-X-5 does not equal 10X-5.
Once you get to the Addition and Subtraction stage of the Order of Operations (aka PEMDAS), which is where we are on the left side, it's good to rewrite the expression as additions. 11-X-5 as additions:
11 + (-X) + (-5)
Now that we have additions we can use the Commutative and Associative Properties to rearrange and regroup the expression any way we choose. And since you can only add like terms, we'll rearrange and regroup the expression to group the like terms together. The terms in 11 + (-X) + (-5) are: 11, -X and -5. Among these the like terms are 11 and -5. So the rearranged and regrouped expression looks like:
(11 + (-5)) + (-X)
or
(-X) + (11 + (-5))
Now we can add the grouped like terms:
(-X) + 6
(Once you get good at this you do not need to write down the "rewrite as additions" and "rearrange and regroup" steps. But even if you don't write it down, this is how you should do these in your head.)
With this correction the equation is now:
(-X) + 6 = 4X - 4 + 14
(-X) + 6 = 4X + 10
Add X to both sides:
6 = 5X + 10
Subtract 10 from both sides:
-4 = 5X
Divide both sides by 5:
-4/5 = X
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