1. **State the problem:** Solve the linear equation $2x + 1 = 7x - 3$ for $x$. 2. **Write down the equation:** $$2x + 1 = 7x - 3$$ 3. **Isolate the variable terms on one side:** Subtract $2x$ from both sides: $$1 = 7x - 3 - 2x$$ Simplify: $$1 = 5x - 3$$ 4. **Isolate the constant term on the other side:** Add $3$ to both sides: $$1 + 3 = 5x$$ Simplify: $$4 = 5x$$ 5. **Solve for $x$ by dividing both sides by 5:** $$x = \frac{4}{5}$$ 6. **Final answer:** $$x = \frac{4}{5}$$ This means the value of $x$ that satisfies the equation is $\frac{4}{5}$ or 0.8.