If $4 \gt \ -3x+8 \gt 2$, what is one possible value of $x-5$ ?

Summary Submit

We can solve for $x$ like you would normally do for equations. Just make sure to add or multiply to all three 'sides' accordingly. Similarly, don't forget to flip the sign when dividing or multiplying by a negative.

$$4 \gt \ -3x+8 \gt 2$$ $$4-8 \gt -3x+8-8 \gt 2-8$$ $$-4 \gt -3x \gt -6$$ $$-\frac{4}{3} \lt x \lt 2$$

We can find a value for $x$ here, or simply solve for $x-5$ directly.

$$-\frac{4}{3} \lt x \lt 2$$ $$-\frac{4}{3}-5 \lt x-5 \lt 2-5$$ $$-6.\overline{3} \lt x-5 \lt -3$$

Out of the options, only $\boxed{-5}$ satisfies our inequality.