SOLUTION: problem: how do i solve a problem with a number outside the absolute value lines? {{{1/2}}}|6-2x|= 3x+1 thank you for you time

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Question 628345: problem: how do i solve a problem with a number outside the absolute value lines?
1%2F2|6-2x|= 3x+1
thank you for you time
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
problem: how do i solve a problem with a number outside the absolute value lines?

1%2F2|6 - 2x|= 3x + 1

Clear the fraction by multiplying both sides by 2

  |6 - 2x| = 6x + 2

There are two cases to consider:

Case 1:  When the value of 6 - 2x has the same value as the right side.

  6 - 2x = 6x + 2
     -8x = -4
       x = 1%2F2

Case 2:  When the value of 6 - 2x has -1 times the value of the right side.

  6 - 2x = -(6x + 2)
  6 - 2x = -6x - 2
      4x = -8
       x = -2

There appear to be two solutions 1%2F2 and -2. 

However we must check them to see that they satisfy the
original equation.

Checking 1%2F2

1%2F2|6 - 2x|= 3x + 1

1%2F2|6 - 2(1%2F2)|= 3(1%2F2) + 1

1%2F2|6 - 1|= 3(1%2F2) + 1

1%2F2|5| = (3%2F2) + 1

1%2F2(5) = 3%2F2 + 2%2F2

5%2F2 = 5%2F2

That checks, so 1%2F2 is a solution.

Checking -2

1%2F2|6 - 2x|= 3x + 1

1%2F2|6 - 2(-2)|= 3(-2) + 1

1%2F2|6 + 4|= -6 + 1

1%2F2|10| = -5

1%2F2(10) = -5

   5 = -5

So -2 is not a solutionh and we discard it.

The only solution is 1%2F2

Edwin