How do you solve -4 <= 1/3x-5<-2?

Apr 28, 2015

Solution: $3 \le x < 9$

To begin with, notice there are two inequalities you've got to solve, which are:
$4 \le \frac{1}{3} x - 5$ and $\frac{1}{3} x - 5 < - 2$

No 1

$- 4 \le \frac{1}{3} x - 5$

This is the same as $\frac{x}{3} - 5 \ge - 4$

$\implies \frac{x}{3} \ge - 4 + 5 \implies \frac{x}{3} \ge 1 \implies x \ge 3$

No 2

$\frac{1}{3} x - 5 < - 2 \implies \frac{x}{3} < - 2 + 5 \implies \frac{x}{3} < 3 \implies x < 9$

Now, combine the two inequalities,

$\implies x \ge 3 , x < 9$

This means that $3 \le x < 9$