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

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Answer 1 · 2016-06-30T23:32:07

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

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

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

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

1-b) $x - 12 = - 2 (x - 1)$ $x-12=-2(x-1)$
$\to 3 x = 12 + 2$ $->3x=12+2$
$\to x = \frac{14}{3}$ $->x=14/3$

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

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

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

Checking the solutions

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

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

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