1. **State the problem:** Solve the inequality $8x + 3 \leq 43$ for $x$. 2. **Write the inequality:** $$8x + 3 \leq 43$$ 3. **Isolate the term with $x$ by subtracting 3 from both sides:** $$8x + \cancel{3} - \cancel{3} \leq 43 - 3$$ $$8x \leq 40$$ 4. **Divide both sides by 8 to solve for $x$:** $$\frac{8x}{\cancel{8}} \leq \frac{40}{\cancel{8}}$$ $$x \leq 5$$ 5. **Interpretation:** The solution to the inequality is all values of $x$ less than or equal to 5. **Final answer:** $$x \leq 5$$