1. **State the problem:** Solve the inequality $\frac{2}{3x+6} < 0$. 2. **Rewrite the inequality:** The denominator is $3x+6$. The fraction is negative when numerator and denominator have opposite signs. 3. **Analyze numerator:** Numerator is 2, which is positive. 4. **Analyze denominator:** For the fraction to be negative, denominator must be negative. 5. **Solve denominator inequality:** $$3x + 6 < 0$$ $$3x < -6$$ $$x < \cancel{3}{3} \times -2$$ $$x < -2$$ 6. **Conclusion:** The solution is all $x$ such that $x < -2$. --- 1. **State the problem:** Solve the inequality $\frac{-23}{4x+8} \geq 0$. 2. **Rewrite the inequality:** Numerator is $-23$, which is negative. 3. **Analyze denominator:** For the fraction to be greater than or equal to zero, denominator must be negative or zero (but zero makes denominator undefined, so exclude zero). 4. **Solve denominator inequality:** $$4x + 8 < 0$$ $$4x < -8$$ $$x < \cancel{4}{4} \times -2$$ $$x < -2$$ 5. **Exclude zero denominator:** $$4x + 8 \neq 0$$ $$4x \neq -8$$ $$x \neq -2$$ 6. **Conclusion:** The solution is all $x$ such that $x < -2$. **Final answers:** - For a) $x < -2$ - For б) $x < -2$