Question: User: 8x−2[3x+(4−2x)]=2(5x+1)
1. **State the problem:** Solve the equation $$8x - 2[3x + (4 - 2x)] = 2(5x + 1)$$ for $$x$$.
2. **Use the distributive property and simplify inside the brackets:**
$$8x - 2[3x + 4 - 2x] = 2(5x + 1)$$
Inside the brackets, combine like terms:
$$3x - 2x = x$$
So,
$$8x - 2[x + 4] = 2(5x + 1)$$
3. **Distribute $$-2$$ over $$x + 4$$:**
$$8x - 2 \cdot x - 2 \cdot 4 = 2(5x + 1)$$
$$8x - 2x - 8 = 2(5x + 1)$$
4. **Simplify the left side:**
$$6x - 8 = 2(5x + 1)$$
5. **Distribute $$2$$ on the right side:**
$$6x - 8 = 10x + 2$$
6. **Bring all terms involving $$x$$ to one side and constants to the other:**
Subtract $$10x$$ from both sides:
$$6x - 10x - 8 = 2$$
$$\cancel{6x} - \cancel{10x} - 8 = 2$$
$$-4x - 8 = 2$$
Add $$8$$ to both sides:
$$-4x - 8 + 8 = 2 + 8$$
$$-4x = 10$$
7. **Solve for $$x$$ by dividing both sides by $$-4$$:**
$$x = \frac{10}{-4} = -\frac{10}{4}$$
Simplify the fraction:
$$x = -\frac{5}{2}$$
**Final answer:** $$x = -\frac{5}{2}$$