To find the value of \( x \) in the given equation \( 6(x+1)-5x=8+2(x-1) \), follow these steps:
1. Expand both sides of the equation:
On the left side:
[tex]\[
6(x + 1) - 5x
\][/tex]
Distribute the \( 6 \):
[tex]\[
6x + 6 - 5x
\][/tex]
Combine like terms:
[tex]\[
x + 6
\][/tex]
On the right side:
[tex]\[
8 + 2(x - 1)
\][/tex]
Distribute the \( 2 \):
[tex]\[
8 + 2x - 2
\][/tex]
Combine like terms:
[tex]\[
2x + 6
\][/tex]
2. Set the simplified expressions from both sides equal to each other:
[tex]\[
x + 6 = 2x + 6
\][/tex]
3. Solve for \( x \):
Subtract \( x \) from both sides to isolate the variable term on one side:
[tex]\[
6 = 2x + 6 - x
\][/tex]
Simplify:
[tex]\[
6 = x + 6
\][/tex]
Subtract \( 6 \) from both sides:
[tex]\[
6 - 6 = x + 6 - 6
\][/tex]
Simplify:
[tex]\[
0 = x
\][/tex]
Therefore, the value of \( x \) is \( 0 \).
The correct answer is:
[tex]\[
0
\][/tex]
