How do you solve for x: # 2|x − 3| + 4 = 6#?

1 Answer
Apr 9, 2018

Answer:

#x=2" or "x=4#

Explanation:

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

#"isolate "|x-3|#

#"subtract 4 from both sides"#

#rArr2|x-3|=2#

#"divide both sides by 2"#

#rArr|x-3|=1#

#color(magenta)"Positive expression"#

#x-3=1rArrx=1+3=4#

#color(magenta)"Negative expression"#

#-(x-3)=1#

#rArr-x+3=1#

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

#color(blue)"As a check"#

Substitute these values into the left side and if equal to the right side then they are the solutions.

#x=2to2|-1|+4=(2xx1)+4=6#

#x=4to2|1|+4=(2xx1)+4=6#

#rArrx=2" or "x=4" are the solutions"#