How do you solve #|4x - 2| = | - x + 5|#?

1 Answer
Apr 2, 2018

Answer:

The solutions are #S={-1, 7/5}#

Explanation:

Let's build a sign chart

#color(white)(aaaa)##x##color(white)(aaaaaaa)##-oo##color(white)(aaaaaaaaa)##1/2##color(white)(aaaaaaaaaa)##5##color(white)(aaaaaaaaa)##+oo#

#color(white)(aaaa)##4x-2##color(white)(aaaaaaa)##-##color(white)(aaaaaa)##0##color(white)(aaaa)##+##color(white)(aaaaaaaa)##+#

#color(white)(aaaa)##-x+5##color(white)(aaaaaa)##+##color(white)(aa)####color(white)(aaaaaaaaa)##+##color(white)(aaaaa)##0##color(white)(aaa)##-#

#color(white)(aaaa)##|4x-2|##color(white)(aaaaaa)##-4x+2##color(white)(aa)####color(white)(aaaa)##4x-2##color(white)(aaaaa)##4x-2#

#color(white)(aaaa)##|-x+5|##color(white)(aaaaaaa)##x-5##color(white)(aa)####color(white)(aaaa)##x-5##color(white)(aaaaa)##-x+5#

Therefore,

In the interval #x in (-oo, 1/2)#

#-4x+2=x-5#

#5x=7#

#x=7/5#

In the interval #x in (1/2, 5)#

#4x-2=x-5#

#3x=-3#

#x=-1#

In the interval #x in (5, +oo)#

#4x-2=-x+5#

#5x=7#

#x=7/5#

Therefore,

the solutions are #S={-1, 7/5}#

graph{(y-|4x-2|)(y-|-x+5|)=0 [-7.11, 8.69, -0.55, 7.35]}