How do you solve and write the following in interval notation: # 2 < 2x + 4 < 10#?

1 Answer
Shwetank Mauria
Jul 14, 2017

#(-1,3)#

Explanation:

As #2 < 2x+4 <10#

we have #2 < 2x+4# or #2-4 < 2x# i.e. #-1 < x#

Further, as #2x+4 < 10#, we have #2x < 6# or #x < 3#

Hence we have #-1 < x < 3#,

which in interval notation can be written as #(-1,3)#

Note: Had it been #-1 <= x < 3#, we would have written #[-1,3)# i.e. for inequality with equality we use square brackets and for pure inequality we use small brackets.

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