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? A.The length of the rods will be greater than 48 inches when x 3 or x

Question

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? 

A.The length of the rods will be greater than 48 inches when x > 3 or x < 7 rods per minute.

gio333 · Answer

B.The length of the rods will be greater than 48 inches when x < 3 or x > 7 rods per minute. C.The length of the rods will be greater than 48 inches when x > –3 or x < –7 rods per minute. D.The length of the rods will be greater than 48 inches when 3 < x < 7 rods per minute.

dumbcow · Answer

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

gio333 · Answer

for the 1st case i got x<3 and 2nd case x>7....right?

dumbcow · Answer

correct

gio333 · Answer

so the answer is B right?