In a scenario where two objects are in a length ratio of 2:1, if each were shortened by 3 inches, what is the length of the longer object in inches?

To determine the length of the longer object in a scenario where two objects have a length ratio of 2:1, we start by defining the lengths of the objects. Let's denote the length of the shorter object as "x." Given the ratio, the length of the longer object will then be "2x."

When both objects are shortened by 3 inches, their new lengths become:

• Shorter object: x - 3

• Longer object: 2x - 3

To maintain the ratio of their lengths after the reduction, we can set up the equation based on their proportions:

(\frac{2x - 3}{x - 3} = 2)

This states that the ratio of the lengths after shortening still holds at 2:1. To solve for x, we cross-multiply:

(2x - 3 = 2(x - 3))

Expanding on the right side, we have:

(2x - 3 = 2x - 6)

Next, isolate the terms:

• Eliminate (2x) from both sides.

• This simplifies to (-3 = -6), leading to:

(-3 + 6 =