Question

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\?
\\( 6 + 2(x + 4) = \frac{1}{2}(3 - x) \\)
\\( 6 + 2(x + 4) = \frac{1}{2}(x - 3) \\)
\\( (6 + 2)(x + 4) = \frac{1}{2}(3 - x) \\)
\\( (6 + 2)(x + 4) = \frac{1}{2}(x - 3) \\)

Explanation:

Step1: Define the number

Let the number be \( x \).

Step2: Translate "twice the sum of a number and four"

The sum of a number (\( x \)) and four is \( x + 4 \). Twice this sum is \( 2(x + 4) \).

Step3: Translate "six added to twice the sum..."

Six added to \( 2(x + 4) \) is \( 6 + 2(x + 4) \).

Step4: Translate "one - half of the difference of three and the number"

The difference of three and the number is \( 3 - x \). One - half of this difference is \( \frac{1}{2}(3 - x) \).

Step5: Set up the equation

Putting it all together, the equation is \( 6+2(x + 4)=\frac{1}{2}(3 - x) \).

Answer:

\( 6 + 2(x + 4)=\frac{1}{2}(3 - x) \) (the first option)