Solve the Problem $\mid \mathrm { C }$ $+ 80 \mid \leq 57$

Solve the problem.
-The temperatures in a freeze-dry process in degrees Celsius roughly satisfy the inequality $\mid \mathrm { C }$ $+ 80 \mid \leq 57$ . What range of temperatures corresponds to this inequality?

A) $\left[ - 23 ^ { \circ } \mathrm { C } , 23 ^ { \circ } \mathrm { C } \right]$
B) $\left[ - 137 ^ { \circ } \mathrm { C } , - 23 ^ { \circ } \mathrm { C } \right]$
C) $\left[ - 137 ^ { \circ } \mathrm { C } , 137 ^ { \circ } \mathrm { C } \right]$
D) $\left[ - 23 ^ { \circ } \mathrm { C } , 137 ^ { \circ } \mathrm { C } \right]$