How do you solve #8abs(x+7)-3=5#?
1 Answer
Explanation:
#"the expression inside the absolute value bars can be"#
#"positive or negative hence we have to consider both"#
#"isolate "|x+7|" by adding 3 to both sides"#
#8|x+7|cancel(-3)cancel(+3)=5+3#
#rArr8|x+7|=8#
#"divide both sides by 8"#
#cancel(8)/cancel(8)|x+7|=8/8#
#rArr|x+7|=1#
#"consider the "color(magenta)" positive value ""of "x+7#
#rArrx+7=1larr"subtract 7 from both sides"#
#rArrx=1-7=-6#
#"consider the "color(magenta)"negative value ""of "x+7#
#rArr-(x+7)=1larr"distribute"#
#rArr-x-7=1larr"add 7 to both sides"#
#rArr-x=1+7=8#
#rArrx=-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=-6to8|-6+7|-3=8-3=5#
#x=-8to8|-8+7|-3=8|-1|-3=8-3=5#
#rArrx=-8" or "x=-6" are the solutions"#
