# How do you solve -2\leq \frac{x - 4}{- 5} < 5?

$- 21 > x \ge 14$

#### Explanation:

Here we have to solve what values of $x$ put us in the range of $- 2 \mathmr{and} 5$. Let's do that. First let's do the lower limit of $- 2$:

$\frac{x - 4}{-} 5 = - 2$

$x - 4 = 10$

$x = 14$

Since the lower limit includes $- 2$, we can say that the value of x is up to and including 14.

Now let's do the upper limit of $5$:

$\frac{x - 4}{-} 5 = 5$

$\left(x - 4\right) = - 25$

$x = - 21$

Since the upper limit of 5 does not include 5 (it's less than but not equal to).

So the values of x that are valid are:

$- 21 > x \ge 14$