How do you solve - 2abs(x - 3) + 10 = - 4?
1 Answer
Feb 8, 2017
Explanation:
Isolate the
color(blue)"absolute value" subtract 10 from both sides.
-2|x-3|cancel(+10)cancel(-10)=-4-10
rArr-2|x-3|=-14 divide both sides by - 2
cancel(-2)/cancel(-2)|x-3|=(-14)/(-2)
rArr|x-3|=7larrcolor(red)"absolute value isolated on left" Equations with an absolute value usually have 2 solutions.
We now solve
x-3=color(red)(+-)7
color(blue)"Solution 1"
x-3=color(red)(+)7rArrx=7+3=10
color(blue)"Solution 2"
x-3=color(red)(-)7rArrx=-7+3=-4
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=10to-2|10-3|+10=-14+10=-4
•x=-4to-2|-4-3|+10=-14+10=-4
rArrx=10" or "x=-4" are the solutions"
