How do you solve and write the following in interval notation: #x − 3>8# AND #x + 2 >#?

1 Answer
Alan P.
Jan 13, 2018

Question is missing a value; see below for an approach using a variable in place of the missing value.

Explanation:

Suppose the intended restrictions were
#{:(x-3 > 8," AND ",x+2 > color(blue)n):}#

Since you can add or subtract the same amount to both sides of an inequality without changing the validity or direction of the inequality,
these are equivalent to
#{:(x > 11," AND ",x > (color(blue)n-2)):}#

Using the notation: #max(a,b)={(a" if " a>=b),(b" if " a < b):}#

Then these restrictions can be combined into the single restriction:
#x > max(8,color(blue)n-2)#
or
in the requested interval notation:
#x in (max(8,color(blue)n-2),+oo)#

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