How do you rewrite this absolute equations

| -5x-1 | = -2X + 12

Would it just be...
-5x-1 = -2x+12
and
5x+1 = -2x+12

or how am I supposed to rewrite the equations?

as you wrote, except the conjunction is "or" not "and"
|-5x - 1| = -2x + 12
-5x - 1 = -2x + 12 or 5x + 1 = -2x + 12
-3x = 13 or 7x = 11
x = -13/3 or x = 11/7

♣♦

no it would always be 5x+1 = -2x+12 in the end, because since the left side is absolute it will always become positive