Using the proportional method, solve for x in the equation 2:x::4:2. What is the value of x?

To solve the proportion represented by the equation 2:x::4:2, we can set up the relationship as follows: ( \frac{2}{x} = \frac{4}{2} ). This indicates that the ratio of the first pair (2 and x) should be equal to the ratio of the second pair (4 and 2).

First, we simplify the right side of the equation: ( \frac{4}{2} = 2 ). Therefore, we have:

[ \frac{2}{x} = 2 ]

To find the value of x, we can cross-multiply:

[ 2 = 2x ]

Now, divide both sides of the equation by 2 to isolate x:

[ x = 1 ]

Thus, the value of x is 1. This means that when we set up our ratios, the original value of 2 relates to 1 in the same way that 4 relates to 2, maintaining the proportionality throughout both pairs of numbers. This is why the answer is indeed 1.