The problem asks us to solve the equation:

$3x + 6(2x - 3) = 4 - 7x$

Step-by-step Solution:

1. Expand the parenthesis: $6(2x - 3) = 12x - 18$ Substitute this into the equation: $3x + 12x - 18 = 4 - 7x$

2. Combine like terms on the left-hand side: $(3x + 12x) - 18 = 4 - 7x$ $15x - 18 = 4 - 7x$

3. Move all terms with $x$ to one side and constants to the other: Add $7x$ to both sides: $15x + 7x - 18 = 4$ $22x - 18 = 4$

   Add $18$ to both sides: $22x = 22$

4. Solve for $x$: Divide both sides by $22$: $x = \frac{22}{22} = 1$

Final Answer:

The solution is $x = 1$, which corresponds to option B.

Do you have any questions or need additional clarifications?

5 Related Questions:

1. How would the solution change if the equation were $3x + 6(2x - 3) = 7x - 4$?
2. What are the steps to check if the solution $x = 1$ satisfies the original equation?
3. How can you graphically represent $3x + 6(2x - 3) = 4 - 7x$?
4. What happens if we add a constant to both sides of the equation? Does the solution change?
5. What is the importance of combining like terms in algebraic equations?

One Tip:

Always simplify expressions by expanding and combining like terms before attempting to isolate the variable. This reduces the risk of errors.