How do you solve #abs(x-3)=2#?

2 Answers
mizoo
Mar 24, 2018

#x = 1, 5#

Explanation:

#|x - 3| = 2#

#x - 3 = +-2#

#x - 3 = 2 => x = 5#
#x - 3 = -2 => x = 1#

Jim G.
Mar 24, 2018

#x=1" or "x=5#

Explanation:

#"the expression inside the absolute value can be positive"#
#"or negative, thus there are 2 possible solutions"#

#color(blue)"Positive"#

#x-3=2rArrx=2+3=5#

#color(blue)"Negative"#

#color(red)(-)(x-3)=2larrcolor(blue)"distribute"#

#-x+3=2#

#rArr-x=2-3=-1rArrx=1#

#color(blue)"As a check"#

#x=5to|5-3|=|2|=2larrcolor(blue)"True"#

#x=1to|1-3|=|-2|=2larrcolor(blue)"True"#

#rArrx=5" or "x=1" are the solutions"#

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