To find the value of [tex]\( x \)[/tex] in the equation
[tex]\[
\frac{x-2}{3} + \frac{1}{6} = \frac{5}{6}
\][/tex]
we need to solve step-by-step. Let's break it down:
1. Eliminate the fractions: To simplify the equation, we can multiply every term by 6 (the common denominator) to clear the fractions.
[tex]\[
6 \left( \frac{x-2}{3} \right) + 6 \left( \frac{1}{6} \right) = 6 \left( \frac{5}{6} \right)
\][/tex]
2. Simplify each term:
- For the first term:
[tex]\[
6 \left( \frac{x-2}{3} \right) = 2(x - 2)
\][/tex]
- For the second term:
[tex]\[
6 \left( \frac{1}{6} \right) = 1
\][/tex]
- For the third term:
[tex]\[
6 \left( \frac{5}{6} \right) = 5
\][/tex]
3. Re-write the equation with the simplified terms:
[tex]\[
2(x - 2) + 1 = 5
\][/tex]
4. Distribute and simplify further:
- Distribute the 2 in the first term:
[tex]\[
2x - 4 + 1 = 5
\][/tex]
- Combine like terms:
[tex]\[
2x - 3 = 5
\][/tex]
5. Solve for [tex]\( x \)[/tex]:
- Add 3 to both sides of the equation:
[tex]\[
2x - 3 + 3 = 5 + 3
\][/tex]
- Simplify the equation:
[tex]\[
2x = 8
\][/tex]
- Divide both sides by 2 to isolate [tex]\( x \)[/tex]:
[tex]\[
x = \frac{8}{2}
\][/tex]
- Simplify:
[tex]\[
x = 4
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is 4. The correct answer is:
A. 4
