Algebra questions with diagrams

A photo frame is a rectangle. Its long side is 2 w plus 5 centimetres, and its short side is 9 centimetres. The perimeter of the frame is 60 centimetres. What is the value of w? Try it first. Pause if you like. Here's the frame. The long side is the length, and it's 2 w plus 5. The short side is the breadth, and it's 9. Opposite sides of a rectangle are equal, so the opposite length is also 2 w plus 5. And the opposite breadth is also 9. Perimeter means all four sides added. Length, plus length, plus breadth, plus breadth. Now put the sides in. 2 w plus 5, plus 2 w plus 5, plus 9, plus 9 — and all of it is 60. Collect the terms with w, and collect the plain numbers. 4 w plus 28 is 60. Minus 28 from the left side, and minus 28 from the right side too, so 4 w is 32. And w is 32 divided by 4, which is 8. So w is 8.