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

2 Answers
Mar 24, 2018

x = 1, 5

Explanation:

|x - 3| = 2

x - 3 = +-2

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

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"