SOLUTION: Solve: 4(x+2)-3x=x-6 I am not sure what the answer means: a) 1 b) Identity c)No solution d) 0 Can you explain to me what identity means please and help me understand this

Question 70535: Solve: 4(x+2)-3x=x-6
I am not sure what the answer means:
a) 1
b) Identity
c)No solution
d) 0
Can you explain to me what identity means please and help me understand this problem, thank you.
Found 3 solutions by stanbon, Smirnov, funmath:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Solve: 4(x+2)-3x=x-6
I am not sure what the answer means:
a) 1
b) Identity
c)No solution
d) 0
---------------
Solve: 4(x+2)-3x=x-6
You start by assuming the "x's" all mean the same number, and you are
going to find that number. You proceed as you were taught to proceed and
get:
4x+8 -3x = x-6
4x-3x-x= -6-8
0x = -14
0= -14
This is a contradiction that resulted from your assumption.
The assumption was wrong; there is no single number which
can replace "x".
Answer: No solution
Cheers,
Stan H.
Answer by Smirnov(15)   (Show Source): You can put this solution on YOUR website!
Well, an identity means that both sides of the equation are the same, or that it can be simplified to 0=0.
The question simplifies to 0=14, so there would be no solution.

Answer by funmath(2933)   (Show Source): You can put this solution on YOUR website!
Solve: 4(x+2)-3x=x-6
I am not sure what the answer means:
a) 1
b) Identity
c)No solution
d) 0
Can you explain to me what identity means please and help me understand this problem, thank you.
If you simplfy completely and both sides are exactly the same it's an identity and there is an infinite number of solutions. No matter what you put in for x both sides will always equal.
If you simplify both sides of the equation and the variables are eliminated, but the numbers that are left are not =, then you have a contradiction. There is no solution if that happens.
Let's start simplifying:
4(x+2)-3x=x-6
4(x)+4(2)-3x=x-6
4x+8-3x=x-6
x+8=x-6
x-x+8=x-x-6
8=-6
This is a contradiction, so there is no solution. "c" on your multiple choice.
Happy Calculating!!!!
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