Let a, b, c and x be real numbers. How is solving  different from solving 

The correct answer is: x=-(b+c)/a,-(b-c)/a Finally, we can observe that the solutions we get from the two given equations are different.

Hint:
|x| is known as the absolute value of x. It is the non-negative value of x irrespective of its sign. The value of absolute value of x is given by

The symbol |.| is pronounced as ‘modulus’. We read |x| as ‘modulus of x’ or ‘mod x’.
We discuss both these cases for the two given equations.
Step by step solution:
The first equation is
|ax| + b = c
Applying the definition of the modulus for ax in the above equation, we get
For ax < 0, we have
-ax + b = c
Solving for x, we get

For ax ≥ 0, we have
ax + b = c
Solving for x, we get

Thus, we get two solutions for x,

The second equation is
|ax + b| = c
We use the definition of modulus,
For ax + b < 0, we have
-(ax + b)=c
Solving for x, we get

For ax + b ≥ 0, we have
ax + b = c
Solving for x, we get

Thus, the two solutions we get are
x = 
Finally, we can observe that the solutions we get from the two given equations are different.
Note:
In the first equation, mod changes the value of only one term, i.e., ax; whereas in the second equation, mod changes the value two terms, ax and b. This results in the change in values of x for both equations.