How do you solve #|-5x + -2| + 3 = 11#?

1 Answer
Jan 26, 2017

Answer:

#x=-2" or " x=6/5#

Explanation:

Equations involving the #color(blue)"absolute value"# have 2 solutions.

Isolate the absolute value, noting that

#-5x+ -2=-5x-2#

subtract 3 from both sides.

#|-5x-2|cancel(+3)cancel(-3)=11-3#

#rArr|-5x-2|=8#

The 2 solutions are obtained by solving #-5x-2=color(red)(+-)8#

#color(blue)"Solution 1"#

#-5x-2=8#

add 2 to both sides.

#-5xcancel(-2)cancel(+2)=8+2#

#rArr-5x=10rArrx=10/(-5)=-2#

#color(blue)"Solution 2"#

#-5x-2=-8#

add 2 to both sides.

#-5x=-8+2#

#rArr-5x=-6rArrx=(-6)/(-5)=6/5#

#color(blue)"As a check"#

#"left side "=|(-5xx-2)-2|+3=|8|+3=8+3=11 ✔︎#

#"left side "=|(-cancel(5)^1xx6/cancel(5)^1)-2|+3#

#=|-6-2|+3=|-8|+3=8+3=11 ✔︎#