To solve the equation [tex]\(\frac{x}{3} + \frac{x}{6} = \frac{7}{2}\)[/tex], follow these steps:
1. Find a common denominator for the fractions on the left side:
- The fractions are [tex]\(\frac{x}{3}\)[/tex] and [tex]\(\frac{x}{6}\)[/tex]. The common denominator for these fractions is 6.
2. Rewrite the fractions with the common denominator:
- [tex]\(\frac{x}{3}\)[/tex] can be rewritten as [tex]\(\frac{2x}{6}\)[/tex].
- [tex]\(\frac{x}{6}\)[/tex] remains as it is.
3. Combine the fractions on the left side:
- Now we have: [tex]\(\frac{2x}{6} + \frac{x}{6}\)[/tex].
- Since they have the same denominator, we can add the numerators: [tex]\(\frac{2x + x}{6} = \frac{3x}{6}\)[/tex].
4. Simplify the combined fraction:
- [tex]\(\frac{3x}{6}\)[/tex] simplifies to [tex]\(\frac{x}{2}\)[/tex].
5. Substitute back into the original equation:
- So the equation simplifies to: [tex]\(\frac{x}{2} = \frac{7}{2}\)[/tex].
6. Solve for [tex]\(x\)[/tex]:
- Since the denominators are the same, you can equate the numerators: [tex]\(x = 7\)[/tex].
Therefore, the solution to the equation [tex]\(\frac{x}{3} + \frac{x}{6} = \frac{7}{2}\)[/tex] is [tex]\(x = 7\)[/tex].
This means the correct answer is:
[tex]\[ x = 7 \][/tex]
