The lengths of a particular type of metal rod are modeled by the equation r = |–24x + 120|, where r represents the lengths of the rod in inches, and x represents the speed at which the rods are produced, in rods per minute. If the manufacturing process is too fast or too slow, the rods will not be long enough. At what speeds will the lengths of the rods be greater than 48 inches?



Since its a absolute value problem, there are 2 cases

−24x+120>48 −24x+120<−48

in either case, the absolute value will be greater than 48 --> |-50| = 50 > 48 Now solve each above equation for x