SOLUTION: How many solutions does this equation have -2(x+7)-5x=-6x-x

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Question 902997: How many solutions does this equation have
-2(x+7)-5x=-6x-x
Found 3 solutions by Edwin McCravy, Stitch, tmwilliamlin168:
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
-2(x+7)-5x = -6x-x
 -2x-14-5x = -7x      <-- we distributed to remove (); combined like terms
    -7x-14 = -7x
       +14      +14   <-- we added 14 to both sides 
   ----------------
    -7x    = -7x+14
     7x       7x      <-- we added 7x to both sides
   ----------------
      0    =     14

Since 0 does not equal to 14 there are no solutions.

Rule:

When all the letters cancel out and there is only a
number left on both sides:

1.  If the numbers on the two sides are EQUAL, there are 
    INFINITELY MANY solutions.  The equation is said to be
    an IDENTITY.

2.  If the numbers on the two sides are BOT equal, there are 
    NO solutions.  The equation is said to be a CONTRADICTION.

Your equation was a CONTRADICTION.

Edwin

Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Given: -2%28X%2B7%29+-+5X+=+-6X+-+X
Let's start by multiplying the -2 through on the left hand side.
-2X+-+14+-+5X+=+-6X+-+X
Combine like terms
-7X+-+14+=+-7X
Add 7X to both sides
-14+=+0
Since -14 is not equal to 0, there are no solutions.
---------------------------------------
You can also check this by graphing the two equations.
Y+=+-2%28X%2B7%29+-+5X
Y+=+-6X+-+X
+graph%28+500%2C+500%2C+-50%2C+50%2C+-50%2C+50%2C+-2%2A%28x%2B7%29-5x%2C+-6x-x%29+
Since the lines do not intersect, there are no solutions

Answer by tmwilliamlin168(27) About Me  (Show Source):
You can put this solution on YOUR website!
It has none.
-2(x+7)-5x=-6x-x
-2x-14-5x=-7x
-7x-14=-7x
-14=0 (which is impossible so there is no solution)