1. **State the problem:** We want to determine if the equation $6x + 9 = hx + 15$ is solvable for $x$. 2. **Understand the equation:** This is a linear equation in $x$ with a parameter $h$. The general form is $ax + b = cx + d$. 3. **Rearrange the equation:** Move all terms involving $x$ to one side and constants to the other: $$6x - hx = 15 - 9$$ which simplifies to $$x(6 - h) = 6$$ 4. **Solve for $x$:** If $6 - h \neq 0$, then $$x = \frac{6}{6 - h}$$ 5. **Check for solvability:** - If $6 - h = 0$, i.e., $h = 6$, then the equation becomes $6x + 9 = 6x + 15$, which simplifies to $9 = 15$, a contradiction, so no solution. - If $h \neq 6$, the equation has a unique solution given by $x = \frac{6}{6 - h}$. **Final answer:** The equation is solvable for all $h$ except $h = 6$, where it has no solution.