-7|2x-2| + 10 = -4

Isolate the absolute value:

Add -10 to both sides:

     -7|2x-2| = -4 - 10

Combine terms on right:

     -7|2x-2| = -14

Divide both sides by -14

       |2x-2| = 2

To get rid of the absolute values we split
it into two equations with OR between them
according to this rule:

|expression| = A 

where A is a non-negative number

splits into 

expression = A  OR expression = -A

(If A is negative there is no solution)

So therefore

       |2x-2| = 2

becomes the two equations with OR between them:

  2x-2 = 2 OR 2x-2 = -2

Then we solve each:

  2x = 2+2 OR 2x = -2+2
  2x = 4   OR 2x = 0
   x = 2   OR  x = 0

So these are the two solutions

Edwin