How do you solve the equation abs(5-6x)=7|5−6x|=7?
1 Answer
Explanation:
"the expression inside the absolute value can be positive or"the expression inside the absolute value can be positive or
"negative"negative
rArr5-6x=color(red)(+-)7⇒5−6x=±7
color(blue)"first solution"first solution
5-6x=color(red)(+)75−6x=+7
"subtract 5 from both sides"subtract 5 from both sides
rArr-6x=2⇒−6x=2
"divide both sides by - 6"divide both sides by - 6
rArrx=2/(-6)=-1/3⇒x=2−6=−13
color(blue)"second solution"second solution
5-6x=color(red)(-)75−6x=−7
"subtract 5 from both sides"subtract 5 from both sides
rArr-6x=-12⇒−6x=−12
"divide both sides by - 6"divide both sides by - 6
rArrx=(-12)/(-6)=2⇒x=−12−6=2
color(blue)"As a check"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=-1/3to|5+2|=|7|=7x=−13→|5+2|=|7|=7
x=2to|5-12|=|-7|=7x=2→|5−12|=|−7|=7
rArrx=-1/3" or "x=2" are the solutions"⇒x=−13 or x=2 are the solutions
