1. **State the problem:** Solve the equation $2(x-7)=8(3x+3)$ for $x$. 2. **Write down the equation:** $$2(x-7)=8(3x+3)$$ 3. **Apply the distributive property:** $$2 \times x - 2 \times 7 = 8 \times 3x + 8 \times 3$$ $$2x - 14 = 24x + 24$$ 4. **Bring all terms involving $x$ to one side and constants to the other:** $$2x - 24x = 24 + 14$$ $$\cancel{2x} - 24x = 24 + 14 - \cancel{2x}$$ $$-22x = 38$$ 5. **Solve for $x$ by dividing both sides by $-22$:** $$x = \frac{38}{-22}$$ $$x = -\frac{38}{22}$$ 6. **Simplify the fraction by dividing numerator and denominator by their greatest common divisor 2:** $$x = -\frac{\cancel{38}^{{19}}}{\cancel{22}^{{11}}}$$ $$x = -\frac{19}{11}$$ **Final answer:** $$x = -\frac{19}{11}$$