1. The problem is to solve the equation $4.6x + 3.4x = 0$ for $x$. 2. Combine like terms on the left side. Since both terms have $x$, add the coefficients: $$4.6x + 3.4x = (4.6 + 3.4)x = 8.0x$$ 3. The equation becomes: $$8.0x = 0$$ 4. To solve for $x$, divide both sides by 8.0: $$x = \frac{0}{8.0} = 0$$ 5. Therefore, the solution to the equation is $x = 0$. This means the only value of $x$ that satisfies the equation is zero.