Question: User: |2x+1| -3=0
1. **State the problem:** Solve the equation $$|2x+1| - 3 = 0$$ for $$x$$.
2. **Isolate the absolute value:** Add 3 to both sides:
$$|2x+1| = 3$$
3. **Recall the definition of absolute value:** For any expression $$A$$, $$|A| = B$$ means $$A = B$$ or $$A = -B$$.
4. **Set up two equations:**
$$2x + 1 = 3$$
$$2x + 1 = -3$$
5. **Solve the first equation:**
$$2x + 1 = 3$$
Subtract 1 from both sides:
$$2x = 3 - 1$$
$$2x = 2$$
Divide both sides by 2:
$$x = \frac{\cancel{2}}{\cancel{2}} = 1$$
6. **Solve the second equation:**
$$2x + 1 = -3$$
Subtract 1 from both sides:
$$2x = -3 - 1$$
$$2x = -4$$
Divide both sides by 2:
$$x = \frac{-4}{2} = -2$$
7. **Final answer:**
$$x = 1 \text{ or } x = -2$$