To solve the equation [tex]\(\frac{x}{2} + \frac{1}{3} = \frac{1}{4}\)[/tex] for [tex]\(x\)[/tex], we'll go through the following step-by-step process:
1. Isolate the term with [tex]\(x\)[/tex]:
Start by subtracting [tex]\(\frac{1}{3}\)[/tex] from both sides of the equation:
[tex]\[
\frac{x}{2} + \frac{1}{3} - \frac{1}{3} = \frac{1}{4} - \frac{1}{3}
\][/tex]
This simplifies to:
[tex]\[
\frac{x}{2} = \frac{1}{4} - \frac{1}{3}
\][/tex]
2. Find a common denominator to combine fractions:
The common denominator between 4 and 3 is 12. Convert the fractions accordingly:
[tex]\[
\frac{1}{4} = \frac{3}{12} \quad \text{and} \quad \frac{1}{3} = \frac{4}{12}
\][/tex]
Now we can subtract the fractions:
[tex]\[
\frac{x}{2} = \frac{3}{12} - \frac{4}{12} = \frac{3 - 4}{12} = \frac{-1}{12}
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], multiply both sides of the equation by 2:
[tex]\[
x = 2 \times \frac{-1}{12} = \frac{-2}{12} = -\frac{1}{6}
\][/tex]
Given this result, the value of [tex]\(x\)[/tex] must be [tex]\(-\frac{1}{6}\)[/tex].
Therefore, the answer is:
C) [tex]\(-\frac{1}{6}\)[/tex]
