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#