How do you solve and write the following in interval notation: #2x> -10# or #x > 1#?

1 Answer
smartspot2
Jan 6, 2018

#(-5,\infty)#

Or, if you want to look cool and smart,

#x in (-5, \infty)#

Explanation:

Simplifying the first inequality:

#2x > -10#
#x > -5#

Note that the second inequality is contained within the first inequality; if #x# is greater than 1, then it must also be greater than -5. Thus, we can just ignore the second inequality.

Putting this into interval notation, the lower bound would be -5, without including -5, and the upper bound is #\infty#:

#x in (-5, \infty)#

The left parentheses is round, since we are excluding -5. The right parentheses is also round, because of convention (and also because infinity is just a concept and not an actual number)

The fancy "E" represents the word "in"; #x in [a, b]# means that #x# is in the interval #[a, b]#.

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