1. **State the problem:** Solve the equation $10x - 2 = -62$ for $x$. 2. **Add 2 to both sides** to isolate the term with $x$: $$10x - 2 + 2 = -62 + 2$$ $$10x = -60$$ 3. **Divide both sides by 10** to solve for $x$: $$\cancel{10}x = \frac{-60}{\cancel{10}}$$ $$x = -6$$ 4. **Final answer:** $x = -6$. This means the value of $x$ that satisfies the equation is $-6$.