SOLUTION: what is the value of X? 5x-(2x+2)=x+(3x-5)

Question 66963This question is from textbook
: what is the value of X?
5x-(2x+2)=x+(3x-5) This question is from textbook

Found 2 solutions by checkley71, bam878s:
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
5x-(2x+2)=x+(3x-5)
5x-2x-2=x+3x-5
3x-x-3x=-5+2
-x=-3
x=3
Answer by bam878s(77) (Show Source): You can put this solution on YOUR website!
From the beginning we have
5x-(2x+2) = x+(3x-5)
5x-2x-2 = x+3x-5
Now that we got rid of those horrible parentheses we can do something with this equation.
Let's start by adding two to both sides:
(5x-2x-2)+2 = (x+3x-5)+2
to get
5x-2x-2+2 = x+3x-5+2
5x-2x = x+3x-3
Now let's add the "x" terms
5x-2x = x+3x-3
3x = 4x-3
Now let's subtract 3x to both sides
3x-3x = (4x-3)-3x
0 = 4x-3-3x
0 = x-3
Now simply add 3 to both sides
0+3 = (x-3)+3
3 = x-3+3
3 = x-0
3=x. You can see by plugging 3 into the original equation that 3 is the correct answer.
The key to problems like these are to utilize the following equalities
For any numbers a,b, and c, we have
a(b+c) = ab+ac
(a+b)c= ab+ac.
These helped alot when we added "x" terms. For instance the fact that 2x+6x=8x may not make since to someone first starting out with algebra. But, to look at it another way and utilizing the above formulas we see
2x+6x = (2+6)x = 8x
When we had 5x-(2x+2), let's first "drop" the 5x and look at just -(2x+2). Well, this is just -1(2x+2). So, using the above formulas, we have -2x-2 when we multiply out the (-1). That is how I got 5x-(2x+2) = 5x-2x-2.
I hope this helps!

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