1. **State the problem:** Solve the linear equation $8x - 3 = 2x + 10$ for $x$. 2. **Formula and rules:** To solve for $x$, we use the properties of equality: we can add, subtract, multiply, or divide both sides of the equation by the same number without changing the equality. 3. **Step 1: Move all terms with $x$ to one side.** Subtract $2x$ from both sides: $$8x - 3 - 2x = 2x + 10 - 2x$$ which simplifies to $$6x - 3 = 10$$ 4. **Step 2: Move constant terms to the other side.** Add $3$ to both sides: $$6x - 3 + 3 = 10 + 3$$ which simplifies to $$6x = 13$$ 5. **Step 3: Solve for $x$.** Divide both sides by $6$: $$x = \frac{13}{6}$$ 6. **Final answer:** $$x = \frac{13}{6}$$ This means the value of $x$ that satisfies the equation is $\frac{13}{6}$.