Question: User: 8w+7=-3w-4
1. **State the problem:** Solve the equation $$8w + 7 = -3w - 4$$ for the variable $$w$$.
2. **Write down the formula and rules:** To solve linear equations, we aim to isolate the variable on one side by performing inverse operations and maintaining equality.
3. **Step 1: Add $$3w$$ to both sides to get all $$w$$ terms on one side:**
$$8w + 3w + 7 = -3w + 3w - 4$$
$$11w + 7 = -4$$
4. **Step 2: Subtract $$7$$ from both sides to isolate the $$w$$ term:**
$$11w + 7 - 7 = -4 - 7$$
$$11w = -11$$
5. **Step 3: Divide both sides by $$11$$ to solve for $$w$$:**
$$w = \frac{-11}{11}$$
6. **Step 4: Simplify the fraction by canceling common factors:**
$$w = \frac{\cancel{11} \times (-1)}{\cancel{11}} = -1$$
**Final answer:** $$w = -1$$