Inspirion 15r is available with two models 7520 and 5520
And back light Keyboard is available with 7520. Assuming that have 7520, would request you to follow the below mentioned steps
Press FN+F6 once to turn on the keyboard back light. Press < FN >< F6 > second time to decrease the brightness of the keyboard back light and pressing < FN >< F6 > for the third time turns off the keyboard back light.
Please reply if you have any further questions
Thanks & Regards