Question: Solve the equation 6x + 7 = 4x + 6 algebraically.
1. **State the problem:** We need to solve the equation $$6x + 7 = 4x + 6$$ for the variable $$x$$.
2. **Write down the equation:** $$6x + 7 = 4x + 6$$
3. **Goal:** Isolate $$x$$ on one side of the equation.
4. **Subtract $$4x$$ from both sides:**
$$6x + 7 - 4x = 4x + 6 - 4x$$
which simplifies to
$$\cancel{6x} + 7 - \cancel{4x} = \cancel{4x} + 6 - \cancel{4x}$$
$$2x + 7 = 6$$
5. **Subtract 7 from both sides:**
$$2x + 7 - 7 = 6 - 7$$
which simplifies to
$$2x + \cancel{7} - \cancel{7} = 6 - 7$$
$$2x = -1$$
6. **Divide both sides by 2 to solve for $$x$$:**
$$\frac{2x}{2} = \frac{-1}{2}$$
which simplifies to
$$\cancel{2}x / \cancel{2} = -\frac{1}{2}$$
$$x = -\frac{1}{2}$$
**Final answer:** $$x = -\frac{1}{2}$$