Can you have muscle weakness in you arm and legs if you have cervical entrapment in your neck and back due to a disk herniation?

Yes. Depending on what vertebral levels are affected, you can have pinching of the nerves as they exit one or both sides of the vertebral column, so one or both sides could be affected.If the disc herniation is toward the spinal cord, esp. in the neck where there is little extra space, the effects could be worse & affect more then the limbs.Weakness/decreased reflexes are an indication for surgery.