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-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