1. **State the problem:** Solve the equation $5x + 2 = 7x$ for $x$. 2. **Write down the formula and rules:** To solve linear equations, we isolate $x$ by moving all terms with $x$ to one side and constants to the other. 3. **Step-by-step solution:** Start with the equation: $$5x + 2 = 7x$$ Subtract $5x$ from both sides to get all $x$ terms on one side: $$\cancel{5x} + 2 = 7x - \cancel{5x} \implies 2 = 2x$$ 4. **Isolate $x$ by dividing both sides by 2:** $$\frac{2}{\cancel{2}} = \frac{2x}{\cancel{2}} \implies 1 = x$$ 5. **Final answer:** $$x = 1$$ This means the value of $x$ that satisfies the equation is 1.