JWhich 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”?

6 + 2(x + 4) = 6 plus 2 left-parenthesis x plus 4 right parenthesis equals StartFraction one-half EndFraction left-parenthesis 3 minus x right-parenthesis.(3 – x)
6 + 2(x + 4) = 6 plus 2 left-parenthesis x plus 4 right parenthesis equals StartFraction one-half EndFraction left-parenthesis x minus 3 right-parenthesis.(x – 3)
(6 + 2)(x + 4) = left-parenthesis 6 plus 2 right-parenthesis left-parenthesis x plus 4 right parenthesis equals StartFraction one-half EndFraction left-parenthesis 3 minus x right-parenthesis.(3 – x)
(6 + 2)(x + 4) = left-parenthesis 6 plus 2 right-parenthesis left-parenthesis x plus 4 right parenthesis equals StartFraction one-half EndFraction left-parenthesis x minus 3 right-parenthesis.(x – 3)

The equation which 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” is option A) 6 + 2(x + 4) = 1/2(3 – x)

We have been given that "six added to twice the sum of a number and four is equal to one-half of the difference of three and the number”. Converting the words into equation we get

Here let x = be the number, then

6 + 2(x + 4) = 1/2(3 – x) (1)

Now as we look into the options,

Option A) is the correct option as it is the same equation as given in equation (1).

Option B) is incorrect as the equation it is stating is 6+2(x+4)= 1/2(x-3) which is not same as equation (1)

Option C) is incorrect as the equation it is stating is (6+2)(x+4)= 1/2(3-x) which is not same as equation (1)

Option D) is incorrect as the equation it is stating is (6+2)(x+4)= 1/2(3-x) which is not same as equation (1)

Hence option A) is the correct answer

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