Question: Solve the inequality and graph the solution.
4(2x + 1) < 4
Graph: a number line with an open circle at -1 and the line shaded to the left. position_hint = bottom-center
1. **State the problem:** Solve the inequality $$4(2x + 1) < 4$$ and graph the solution on a number line.
2. **Use the distributive property:** Multiply $$4$$ by each term inside the parentheses:
$$4 \times 2x + 4 \times 1 < 4$$
which simplifies to
$$8x + 4 < 4$$
3. **Isolate the variable term:** Subtract $$4$$ from both sides:
$$8x + 4 - 4 < 4 - 4$$
which simplifies to
$$8x < 0$$
4. **Divide both sides by 8:**
$$\frac{8x}{\cancel{8}} < \frac{0}{\cancel{8}}$$
which simplifies to
$$x < 0$$
5. **Interpret the solution:** The inequality $$x < 0$$ means all values less than zero satisfy the inequality.
6. **Graph the solution:** On a number line, draw an open circle at $$0$$ (since $$x$$ cannot equal $$0$$) and shade all values to the left of $$0$$.
**Note:** The user mentioned an open circle at $$-1$$ and shading to the left, but the solution is $$x < 0$$, so the open circle should be at $$0$$.
**Final answer:** $$x < 0$$