How do you solve #2abs(6-2x)-1=7#?

1 Answer
Oct 16, 2016

Answer:

#x=1# and #x=5#

Explanation:

#2abs(6-2x)-1=7#

Isolate the absolute value part of the equation.

#2abs(6-2x)-1=color(white)a7#
#color(white)(aaaaaaa^2)+1color(white)(a)+1color(white)(aaa)#Add 1 to both sides

#(2abs(6-2x))/2color(white)(a^2a)=color(white)a8/2color(white)(aaa)#Divide both sides by 2

#abs(6-2x)=4#

Solving absolute value problems requires setting up TWO equations. Make the right side of the 2nd equation negative.

#color(white)(a^2)6-2x=4color(white)(aaa)#and#color(white)(aaa)6-2x=-4#
#-6color(white)(aaaaa)-6color(white)(aaaaaa)-6color(white)(aaaaaa^2a)-6color(white)(aa)#Subtract 6

#(-2x)/-2=(-2)/-2color(white)(aaa)#and#color(white)(aa)(-2x)/-2=(-10)/-2color(white)(aa)#Divide by -2

#color(white)(aa)x=1color(white)(aaaaaaa)#and#color(white)(aaaaaa)x=5#