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

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Answer 1 · 2016-09-21T10:31:21

$-21>x>=14$

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

$(x-4)/-5=-2$

$x-4=10$

$x=14$

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 $5$ :

$(x-4)/-5=5$

$(x-4)=-25$

$x=-21$

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:

$-21>x>=14$

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