a moving company charges $840 plus $17 per hour. Another moving company charges $760 plus $22 per hour. How long is a job that costs the same no matter which company is used?

Equation:  840+17x=760+22x     
Solve for x  x=16 see proof.
17 x + 840 = 22 x + 760
Subtract 22 x from both sides:
(17 x - 22 x) + 840 = (22 x - 22 x) + 760
17 x - 22 x = -5 x:
-5 x + 840 = (22 x - 22 x) + 760
22 x - 22 x = 0:
840 - 5 x = 760
Subtract 840 from both sides:
(840 - 840) - 5 x = 760 - 840
840 - 840 = 0:
-5 x = 760 - 840
760 - 840 = -80:
-5 x = -80
Divide both sides of -5 x = -80 by -5:
(-5 x)/(-5) = (-80)/(-5)
(-5)/(-5) = 1:
x = (-80)/(-5)
The gcd of -80 and -5 is -5, so (-80)/(-5) = (-5×16)/(-5×1) = (-5)/(-5)×16 = 16:
Answer:  x = 16