Question

The length of a picture frame is 7 inches more than the width. For what values of x is the perimeter of the picture frame greater than 150 inches.

Answer 1

x is greater than 34 inches.

Explanation:

Let x = width, then the length = x+7 inches.

Perimeter = 2(W + L) = 2(x + x + 7) = 4x + 14 , so:

4x + 14 > 150

4x > 150 - 14

4x > 136

x > 34.

Answer 2

x > 34

Explanation:

Let x be the width of the picture frame

It then follows that the length = x + 7

Therefore, our inequality is:

`2(x+7) +2x > 150\\2x+14+2x > 150\\4x > 136\\x > 34`

For all values of x greater than 34 the perimeter is greater than 150 inches.