How do you solve 8abs(x+7)-3=5?
1 Answer
May 3, 2018
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"
