How do you solve #abs(11+2x)=5#?

1 Answer
May 23, 2018

Answer:

#x=-8" or "x=-3#

Explanation:

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

#color(magenta)"positive expression"#

#11+2x=5#

#"subtract 11 from both sides and divide by 2"#

#2x=5-11=-6rArrx=(-6)/2=-3#

#color(magenta)"negative expression"#

#-(11+2x)=5larr"distribute"#

#-11-2x=5#

#"add 11 to both sides and divide by "-2#

#-2x=5+11=16rArrx=16/(-2)=-8#

#color(blue)"As a check"#

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

#x=-3to|11-6|=|5|=5#

#x=-8to|11-16|=|-5|=5#

#x=-8" or "x=-3" are the solutions"#