How do you graph and solve |x-5|+|2-2x|=7 |x5|+|22x|=7?

1 Answer
Jun 30, 2016

x = {0,4}x={0,4}

Explanation:

abs(x-5)=7-2abs(x-1)|x5|=72|x1| gives

1) x-5=7-2abs(x-1)x5=72|x1|
->x-12=2abs(x-1)x12=2|x1|

1-a) x-12=2(x-1)x12=2(x1)
->-12=x-212=x2
->x=10x=10

1-b) x-12=-2(x-1)x12=2(x1)
->3x=12+23x=12+2
->x=14/3x=143

2) -(x-5)=7-2abs(x-1)(x5)=72|x1|
->-x-2=-2abs(x-1)x2=2|x1|
->x+2=2abs(x-1)x+2=2|x1|

2-a) x+2=2(x-1)x+2=2(x1)
->2=x-22=x2
->x=4x=4

2-b) x+2=-2(x-1)x+2=2(x1)
->3x+2=23x+2=2
->x=0x=0

Checking the solutions

x = {-14/3,0,4,10}x={143,0,4,10}

we keep the very solutions: x = {0,4}x={0,4}