Answer
$-2 \leq x \leq 7$
Work Step by Step
$y = 3 - |2x - 5|$; and $y$ is $at$ $least$ $-6$.
Since we already have a condition for $y$ which can be modeled as $y\geq -6$, we can re-write the original equation as follows: $$y = 3 - |2x - 5|$$ $$-6\leq 3 - |2x - 5|$$ and now solve for $x$: $$|2x - 5| \leq 3 + 6$$ $$|2x - 5| \leq 9$$ $$2x - 5\leq 9$$ $$OR$$ $$2x -5\geq -9$$ Solving each individually: $$2x \leq 9 + 5$$ $$x \leq \frac{14}{2}$$ $$x \leq 7$$ $$OR$$ $$2x \geq -9 + 5$$$$x\geq \frac{-4}{2}$$ $$x\geq -2$$ Therefore, the solution set for $x$ that satisfies all conditions established is $-2 \leq x \leq 7$
