Final answer:
To solve for x in a proportion involving a scale factor, we set up the equation corresponding to the given scale factor ratio and solve for x using cross-multiplication and algebraic manipulation. The original question seems to have a typo, which makes solving it as presented uncertain.
Step-by-step explanation:
The student's question involves solving for x when given a ratio that represents a scale factor. Given the scale factor from A to B is 2:7, we have the equation 8x - 7 (B) = 14 (A). To solve for x, we use the concept of proportions that equate the scale factor to the ratio of the corresponding sides or measurements. A problem of similar nature can involve finding an actual dimension when given the scale measurement and the scale factor. For example, using the proportion 1:2 = 4:x, we can find the value of x by setting up the proportion such that 1/2 = 4/x, leading to x = 8.
Another example involves determining the side length of a square when scaled up by a factor. For instance, if a square's side length is 4 inches and the scale factor is 2, then the side length of the larger square is 4 inches × 2 = 8 inches.
To solve our original problem, the proportion 2/7 = 14/(8x - 7) must be used. We can cross multiply to get 2 × (8x - 7) = 14 × 7. Simplifying this gives us 16x - 14 = 98, and solving for x gives us x = 7. However, the initial equation seems to be misinterpreted, and without further clarification, we cannot confirm the solution of x as 1/4 or the scale factor as 1:4.