How do you solve #- 5| x + 1| = -10#?

1 Answer
Jim G.
Nov 24, 2017

#x=1" or "x=-3#

Explanation:

#"divide both sides by "-5#

#cancel(-5)/cancel(-5)|x+1|=(-10)/(-5)#

#rArr|x+1|=2#

#"the value inside the absolute value function can"#
#"be positive or negative"#

#"hence there are 2 possible solutions"#

#color(blue)"first solution"#

#x+1=2rArrx=2-1=1#

#color(blue)"second solution"#

#-(x+1)=2#

#rArr-x-1=2#

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

#color(blue)"As a check"#

#x=1to-5|2|=-5xx2=-10larr"True"#

#x=-3to-5|-3+1|=-5|-2|==-10larr"True"#

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