Which equation can be used to represent six added to twice the sum of a number and four is equal to one-half of the difference of three and the number?

Six added to twice the sum of a number and four is equal to one-half of the difference of thee and the number.

Let x be the number.

6 + 2 (x + 4) = 1/2 * (3-x)

Find the value of x.

6 + 2x + 8 = 3/2 - x/2

2x + x/2 = 3/2 - 8 - 6

2x + x/2 = 3/2 - 14

2 (2x + x/2) = 2 (3/2 - 14)

4x + x = 3 - 28

5x = - 25

x = - 25/5

x = - 5

To check: x = - 5

6 + 2 (x + 4) = 1/2 * (3-x)

6 + 2 (-5+4) = 1/2 * (3 - (-5))

6 + 2 (-1) = 1/2 * (3 + 5)

6 - 2 = 1/2 (8)

4 = 4