Let's solve the equation step-by-step to find the value of [tex]\( x \)[/tex] in the given equation:
[tex]\[ 6(x + 1) - 5x = 8 + 2(x - 1) \][/tex]
First, we need to expand both sides:
1. Expand the left side:
[tex]\[ 6(x + 1) - 5x \][/tex]
[tex]\[ = 6x + 6 - 5x \][/tex]
[tex]\[ = x + 6 \][/tex]
2. Expand the right side:
[tex]\[ 8 + 2(x - 1) \][/tex]
[tex]\[ = 8 + 2x - 2 \][/tex]
[tex]\[ = 2x + 6 \][/tex]
Now, rewrite the equation with the expanded terms:
[tex]\[ x + 6 = 2x + 6 \][/tex]
Next, we want to isolate [tex]\( x \)[/tex] on one side of the equation. Subtract [tex]\( x \)[/tex] from both sides:
[tex]\[ 6 = x + 6 \][/tex]
Then, subtract 6 from both sides:
[tex]\[ 0 = x \][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex].
Thus, the correct answer is:
[tex]\[ 0 \][/tex]
