1. **State the problem:** Solve the inequality $$\frac{2 - x}{x + 3} \geq 4$$ and give the solutions correct to 3 significant figures. 2. **Rewrite the inequality:** Move all terms to one side to compare with zero: $$\frac{2 - x}{x + 3} - 4 \geq 0$$ 3. **Find a common denominator and simplify:** $$\frac{2 - x}{x + 3} - \frac{4(x + 3)}{x + 3} \geq 0$$ $$\frac{2 - x - 4(x + 3)}{x + 3} \geq 0$$ 4. **Expand the numerator:** $$2 - x - 4x - 12 = 2 - 5x - 12 = -5x - 10$$ 5. **Rewrite the inequality:** $$\frac{-5x - 10}{x + 3} \geq 0$$ 6. **Factor numerator:** $$\frac{-5(x + 2)}{x + 3} \geq 0$$ 7. **Analyze the inequality:** The expression changes sign at points where numerator or denominator is zero: at $$x = -2$$ and $$x = -3$$. 8. **Determine intervals:** - Interval 1: $$(-\infty, -3)$$ - Interval 2: $$(-3, -2)$$ - Interval 3: $$(-2, \infty)$$ 9. **Test each interval:** - For $$x = -4$$ in Interval 1: $$\frac{-5(-4 + 2)}{-4 + 3} = \frac{-5(-2)}{-1} = \frac{10}{-1} = -10 < 0$$ (False) - For $$x = -2.5$$ in Interval 2: $$\frac{-5(-2.5 + 2)}{-2.5 + 3} = \frac{-5(-0.5)}{0.5} = \frac{2.5}{0.5} = 5 > 0$$ (True) - For $$x = 0$$ in Interval 3: $$\frac{-5(0 + 2)}{0 + 3} = \frac{-5(2)}{3} = \frac{-10}{3} = -3.33 < 0$$ (False) 10. **Check points where expression is zero or undefined:** - At $$x = -2$$ numerator zero, expression zero, included since inequality is $$\geq 0$$. - At $$x = -3$$ denominator zero, expression undefined, exclude. 11. **Final solution:** $$-3 < x \leq -2$$ **Answer:** The solution to the inequality correct to 3 significant figures is $$x \in (-3, -2]$$.