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

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Answer 1 · 2016-06-30T23:32:07

$x = {0,4}$

$abs(x-5)=7-2abs(x-1)$ gives

1) $x-5=7-2abs(x-1)$
$->x-12=2abs(x-1)$

1-a) $x-12=2(x-1)$
$->-12=x-2$
$->x=10$

1-b) $x-12=-2(x-1)$
$->3x=12+2$
$->x=14/3$

2) $-(x-5)=7-2abs(x-1)$
$->-x-2=-2abs(x-1)$
$->x+2=2abs(x-1)$

2-a) $x+2=2(x-1)$
$->2=x-2$
$->x=4$

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

Checking the solutions

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

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

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