Let x be the width of the picture frame. Then, the length of the picture frame is x + 7. The perimeter of the picture frame is 2(x + x + 7) = 4x + 14. To find the values of x for which the perimeter of the picture frame is greater than 150 inches, we solve the inequality 4x + 14 > 150. Subtracting 14 from both sides gives 4x > 136. Dividing both sides by 4 gives x > 34. Therefore, the values of x for which the perimeter of the picture frame is greater than 150 inches are x > 34.