To find the value of $x$, we can set $a$ equal to $b$ since both expressions represent the same variable.

Given: $a = 3x + 12$ $b = 9x - 24$

Setting them equal: $3x + 12 = 9x - 24$

Now, solve for $x$:

1. Subtract $3x$ from both sides: $12 = 6x - 24$

2. Add $24$ to both sides: $36 = 6x$

3. Divide both sides by $6$: $x = 6$

Thus, $x$ equals $6$.

Would you like further details or have any questions? Here are some related questions you might consider:

1. How do you graph the equations $a$ and $b$?
2. What happens if $a$ and $b$ are equal to a different constant?
3. How can we verify the solution for $x$?
4. What are some real-life applications of solving such equations?
5. How would the solution change if the coefficients were different?

Tip: Always check your solution by substituting back into the original equations to ensure both sides are equal.