|3w + 4| = 6w + 1 (absolute value equations. With work to explain it please..

w= 1 and w= -5/9

Step-by-step explanation:

Because you have an absolute value that means that there are 2 possibilities

either (3x +4) is positive or negative. Will work each case and that will give us the answers.

If (3x+4) is positive we have the equation

3w+ 4 = 6w +1 , subtract 3w from both sides

       4 = 6w-3w+1, subtract 1 from both sides

    4-1 = 6w-3w, combine like terms

      3 = 3w , divide both sides by 3

      1 = w

If (3x+4) is negative we have the equation

-(3w+ 4) = 6w +1 , distribute the negative sign in parentheses

  -3w -4 = 6w +1, add 3w and subtract 1 from both sides of the equation

      -4 -1 = 6w +3w, combine like terms

          -5 = 9w , divide both sides by 9

    (-5/9) = w

w = -1

Step-by-step explanation:

(Possibility 1)

3w + 4 = 6w + 1

-6w         -6w

-3w + 4 = 1

      -4     -4

-3w = -3

/-3     /-3

w = -1

(Possibility 2)

3w + 4 = −6w - 1

+6w        +6w

9w + 4 = -1

      -4    -4

9w = -5

/9      /9

w = -5/9

Check:

When you plug w = 1 back into the equation, IT WORKS.

When you plug w = -5/9 back into the equation, IT DOESN'T WORK.

So, w = 1 is the solution to |3w + 4| = 6w + 1