What value or values of x satisfy 2|x+5.3|=4.2

a. x can only equal –3.2.
b. x can only equal 7.4.
c. x can equal –3.2 or –7.4.
d. x can equal –3.2 or 7.4.

2|x+5.3| = 4.2 is equivalent to

(1) 2(x+5.3) = 4.2 when x+5.3 >= 0
solve x = -3.2 when x >= -5.3 ... good value
('good value' means the value has no conflict with the condition -- when)

and

(2) 2[-(x+5.3)] = 4.2 when x+5.3 < 0
solve x = -7.4 when x < -5.3 ... also good

x = -3.2 or -7.4