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"#