How do you solve and write the following in interval notation: #-3 ≤ (x − 4) / 2 <4#?

2 Answers
Jul 14, 2016

Answer:

#x# will be in the interval #[-2, 12)#.

Explanation:

When manipulating an inequality, we can treat it as a three part equation. Whenever we alter one part, we do the same to the other two. This allows us to manipulate the equation like so:
#-3 ≤ (x − 4) / 2 < 4#
#-6 ≤ x − 4 < 8#
#-2 ≤ x < 12#

So the final answer is that #x# will be in the interval #[-2, 12)#.

Jul 14, 2016

Answer:

#x in[-2,12[#

Explanation:

First, you can multiply all terms by 2:

#-6<=x-4<8#

and then you can add 4 to all terms:

#-2<=x<12#