Let's solve the equation $x + 3(x - 1) = 6 - 4(2x + 3)$.

Step 1: Expand both sides of the equation.

On the left-hand side: $x + 3(x - 1) = x + 3x - 3 = 4x - 3$

On the right-hand side: $6 - 4(2x + 3) = 6 - 8x - 12 = -8x - 6$

Step 2: Now the equation becomes:

$4x - 3 = -8x - 6$

Step 3: Combine like terms.

Move all terms with $x$ to one side: $4x + 8x = -6 + 3$ $12x = -3$

Step 4: Solve for $x$:

$x = \frac{-3}{12} = -\frac{1}{4}$

Final Answer:

$x = -\frac{1}{4}$

Would you like more details on any part of this solution?

Here are 5 related questions for further practice:

1. Solve $2x + 4(3x - 2) = 5 - 3(2x + 1)$.
2. Solve $x + 2(x - 3) = 5 - 3(4x + 2)$.
3. What happens if $x + 3 = 2x - 5$?
4. Simplify $5x + 2(3x + 4) = 20 - 6(2x - 1)$.
5. Solve the equation $x - 4 = \frac{2x + 6}{3}$.

Tip:

Always simplify the equation step-by-step, starting by distributing and combining like terms before moving variables to one side!