How do you solve #- 2abs(x - 3) + 10 = - 4#?

1 Answer
Feb 8, 2017

Answer:

#x=10" or "x=-4#

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"#