X Intercepts Absolute E6Fb38

1. **State the problem:** Find the x-intercepts of the function $$g(x) = -2|x + 1| + 4$$. The x-intercepts occur where $$g(x) = 0$$. 2. **Set the function equal to zero:** $$0 = -2|x + 1| + 4$$ 3. **Isolate the absolute value term:** $$-2|x + 1| = -4$$ Divide both sides by $$-2$$: $$|x + 1| = \cancel{-2}\frac{-4}{\cancel{-2}} = 2$$ 4. **Solve the absolute value equation:** $$|x + 1| = 2$$ means $$x + 1 = 2$$ or $$x + 1 = -2$$ 5. **Find the solutions:** - For $$x + 1 = 2$$: $$x = 2 - 1 = 1$$ - For $$x + 1 = -2$$: $$x = -2 - 1 = -3$$ 6. **Conclusion:** The x-intercepts are $$x = -3$$ and $$x = 1$$. Therefore, the correct answer is Option B: $$x = -3$$ and $$x = 1$$.