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

Explanation:

Step1: Define the variable

Let the number be \( x \).

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

The sum of a number and four is \( x + 4 \), twice that 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 that is \( \frac{1}{2}(3 - x) \).

Step5: Set the two expressions equal

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 fourth option)