How do you solve |-5x + -2| + 3 = 11?
1 Answer
Jan 26, 2017
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 ✔︎
