To solve the equation [tex]\( w + \frac{1}{2} = \frac{1}{4} w + 2 \)[/tex], we will follow a step-by-step approach:
1. Eliminate the fractions:
To make the equation easier to work with, let's first eliminate the fractions by multiplying every term by 4, which is the least common multiple of the denominators (2 and 4).
[tex]\[
4 \left( w + \frac{1}{2} \right) = 4 \left( \frac{1}{4} w + 2 \right)
\][/tex]
Simplifying both sides gives:
[tex]\[
4w + 2 = w + 8
\][/tex]
2. Rearrange the equation:
Next, we want to collect all the [tex]\( w \)[/tex] terms on one side and the constant terms on the other side. Subtract [tex]\( w \)[/tex] from both sides:
[tex]\[
4w - w + 2 = 8
\][/tex]
Simplifying gives:
[tex]\[
3w + 2 = 8
\][/tex]
3. Isolate [tex]\( w \)[/tex]:
Subtract 2 from both sides to isolate the term with [tex]\( w \)[/tex]:
[tex]\[
3w = 6
\][/tex]
4. Solve for [tex]\( w \)[/tex]:
Finally, divide both sides by 3 to solve for [tex]\( w \)[/tex]:
[tex]\[
w = 2
\][/tex]
Therefore, the solution for the equation [tex]\( w + \frac{1}{2} = \frac{1}{4} w + 2 \)[/tex] is [tex]\( w = 2 \)[/tex].
The correct answer is:
[tex]\[ w = 2 \][/tex]
