Question: 2(x + 7) = -4x + 14 solve the same way
1. **State the problem:** Solve the equation $$2(x + 7) = -4x + 14$$ for $$x$$.
2. **Write the formula and rules:** Use the distributive property to expand expressions and then combine like terms. Remember to isolate $$x$$ by performing inverse operations step-by-step.
3. **Expand the left side using distributive property:**
$$2(x + 7) = 2 \times x + 2 \times 7 = 2x + 14$$
4. **Rewrite the equation:**
$$2x + 14 = -4x + 14$$
5. **Add $$4x$$ to both sides to get all $$x$$ terms on one side:**
$$2x + 14 + 4x = -4x + 14 + 4x$$
$$\cancel{2x} + 4x + 14 = \cancel{-4x} + 14 + 4x$$
$$6x + 14 = 14$$
6. **Subtract 14 from both sides to isolate $$x$$ term:**
$$6x + 14 - 14 = 14 - 14$$
$$6x + \cancel{14} - \cancel{14} = \cancel{14} - \cancel{14}$$
$$6x = 0$$
7. **Divide both sides by 6 to solve for $$x$$:**
$$\frac{6x}{6} = \frac{0}{6}$$
$$\cancel{6}x/\cancel{6} = 0$$
$$x = 0$$
**Final answer:** $$x = 0$$