How do you solve and write the following in interval notation: #-2 ≤ x + 4 # OR #-1 + 3x > -8#?

1 Answer
KillerBunny
May 26, 2018

#[-6,\infty)#

Explanation:

You can rewrite #-2 \le x+4# as

#-2-4 \le x+4-4 \implies -6 \le x \implies x \ge -6#

Similarly, rewrite #-1+3x>-8# as

#-1+3x+1>-8+1 \implies 3x>-7 \implies x> -7/3#

Since #-6< -7/3#, any number which is greater than #-7/3# will automatically be greater than #-6#. And since the OR condition requires at least one of the conditions to be true, it is sufficient to ask #x \ge -6#

To write it in interval notation, we must find the boundaries of the desired region. We want #x# to be greater than #-6#, but we have no upper bound, which means it's #\infty#.

So, the interval is #[-6,\infty)#

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