1/w - 1 = - 8
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That simply means that you divide w by 8. This can be written as w/8, or as (1/8)w.
Let w equal the width and l equal the length of the rectangle. This means that 2w+2l=135 and since the rectangle has a scale factor of 8:1, that w/l=8. We now have a system of equations. Solve the second equation for w and find that w=8l. Substitute this into the first equation and find that 2(8l)+2l=135, which simplifies to 18l=135. Solve for l to get l=7.5 units. Plug this into either of the original equations to find that w=60 units. The dimensions of the rectangle are 60 by 7.5 units.
It could be either, depending on what x equals. If x = 9, 8 will solve the first one. If x = 1, 8 will solve the second one.
w^2 +/- 28w - 1 is an expression, not an equation. Expressions do not have solutions.
8*w*w*w*w = 8w^4