1. **State the problem:** Solve the equation $32 + 4x = 25 + 5x$ for $x$. 2. **Write down the equation:** $$32 + 4x = 25 + 5x$$ 3. **Isolate the variable terms on one side:** Subtract $4x$ from both sides: $$32 = 25 + 5x - 4x$$ Simplify: $$32 = 25 + x$$ 4. **Isolate $x$:** Subtract $25$ from both sides: $$32 - 25 = x$$ Simplify: $$7 = x$$ 5. **Final answer:** $$x = 7$$ This means the value of $x$ that satisfies the equation is 7.