How do you solve # abs(x+5)>12#?
1 Answer
Aug 31, 2015
Explanation:
You're dealing with the absolute value of an expression, which means that you need totake into account the fact that the absolute value of a real number returns a positive value regardless of the sign of said number.
#color(blue)(|x| = {(x", "x >=0),(-x", "x<0) :}, " "(AA)x in RR)#
This means that you have to look at two possible scenarios, one in which the expression inside the modulus is positive and one in which it's negative.
#x+5 >0 implies |x+5| = x + 5#
The inequality takes the form
#x + 5 >12 implies x > 7#
#x+5<0 implies |x+5| = -(x+5)#
This time, you get
#-(x+5) > 12#
#-x - 5 > 12#
#-x > 17 implies x < -17#
The inequality will be true for any value of
