a) \( x+12=6-3 x \)

To solve the equation \( x + 12 = 6 - 3x \), you can start by getting all terms involving \( x \) on one side and constants on the other. First, add \( 3x \) to both sides to obtain \( x + 3x + 12 = 6 \), which simplifies to \( 4x + 12 = 6 \). Next, subtract 12 from both sides, leading to \( 4x = 6 - 12 \) or \( 4x = -6 \). Finally, divide by 4 to find \( x = -\frac{3}{2} \) or \( -1.5 \). Now that you have the solution, remember that every solution tells a story! Here, you learned how to isolate \( x \) and manipulate equations, skills that are invaluable in algebra. Each mathematical operation is like a dance move—perform them correctly, and you’ll master the rhythm of solving equations! Want to take this further? Try plotting the function \( y = x + 12 \) and \( y = 6 - 3x \) on a graph! The intersection point of the two lines represents the solution to the equation. This visual representation not only reinforces your algebraic skills but also develops your understanding of functions and their relationships. Happy graphing!