Question: User: 5 + 3x=x
1. **State the problem:** Solve the equation $$5 + 3x = x$$ for $$x$$.
2. **Isolate the variable:** To solve for $$x$$, we want to get all terms containing $$x$$ on one side and constants on the other.
3. Subtract $$x$$ from both sides:
$$5 + 3x - x = x - x$$
which simplifies to
$$5 + \cancel{3x} - \cancel{x} = \cancel{x} - \cancel{x}$$
$$5 + 2x = 0$$
4. Subtract $$5$$ from both sides:
$$5 + 2x - 5 = 0 - 5$$
which simplifies to
$$\cancel{5} + 2x - \cancel{5} = -5$$
$$2x = -5$$
5. Divide both sides by $$2$$ to solve for $$x$$:
$$\frac{2x}{2} = \frac{-5}{2}$$
which simplifies to
$$\cancel{2}x/\cancel{2} = -\frac{5}{2}$$
$$x = -\frac{5}{2}$$
**Final answer:** $$x = -\frac{5}{2}$$