To solve the equation [tex]\( 3(2x - 4) = 3x - 5(x + 1) \)[/tex], let's go through each step methodically and apply algebraic principles.
1. Distribute over both terms inside the parenthesis on both sides of the equation:
[tex]\[
3(2x - 4) = 6x - 12
\][/tex]
[tex]\[
-5(x + 1) = -5x - 5
\][/tex]
So, substituting back into the equation, we get:
[tex]\[
6x - 12 = 3x - 5x - 5
\][/tex]
2. Combine like terms on the right side:
[tex]\[
3x - 5x = -2x
\][/tex]
Substituting back into the equation, we get:
[tex]\[
6x - 12 = -2x - 5
\][/tex]
3. Isolate the variable terms on one side. Add [tex]\(2x\)[/tex] to both sides to get all x terms on one side:
[tex]\[
6x + 2x - 12 = -5
\][/tex]
4. Combine like terms on the left side:
[tex]\[
8x - 12 = -5
\][/tex]
5. Isolate the constant term on one side. Add [tex]\(12\)[/tex] to both sides to get rid of the constant term on the left:
[tex]\[
8x - 12 + 12 = -5 + 12
\][/tex]
Simplifies to:
[tex]\[
8x = 7
\][/tex]
6. Solve for [tex]\(x\)[/tex] by dividing both sides by 8:
[tex]\[
x = \frac{7}{8}
\][/tex]
Therefore, the solution to the equation [tex]\( 3(2x - 4) = 3x - 5(x + 1) \)[/tex] is:
[tex]\[
\boxed{\frac{7}{8}}
\][/tex]
The correct answer is [tex]\( \boxed{B} \)[/tex].
