How do you solve and write the following in interval notation: # -8< -2x – 1 ≤ -5#?

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Answer 1 · 2018-07-16T14:34:19

#[2,7/2)#

Remember, we want only an #x# in the middle on the inequality, so whatever we do, we must to it to all three parts.

We can start by adding #1# to all three parts to get

#-7<-2x<=-4#

To get just an #x# in the middle, we can divide all parts by #-2#. Recall that dividing or multiplying by a negative flips the signs. We get

#7/2>x>=2#, which is the same as #2<=x<7/2#. In interval notation, we can write this as

#[2,7/2)#

Note that the bracket means we include the bound, and the parenthesis means we don't include it.

This is the same as saying all values between #x=2# and #x=7/2#, including #2# and not including #7/2#.

Hope this helps!