Question

Calculați
$|x - 1| - 2 |x - 2| = 3$
x E R

Answer 1

$|x - 1| - 2 |x - 2| = 3$

$1)x - 1 - 2(x - 2) = 3$

$x - 1 - 2x + 4 = 3$

$x - 2x = 3 + 1 - 4$

$- x = 0 \: | \times ( - 1)$

$x = 0\:\in\:\mathbb{R}$

$2) - (x - 1) + 2(x - 2) = 3$

$- x + 1 + 2x - 4 = 3$

$- x + 2x = 3 - 1 + 4$

$x = 6\:\in\:\mathbb{R}$

$3) - (x - 1) - 2(x - 2) = 3$

$- x + 1 - 2x + 4 = 3$

$- x - 2x = 3 - 1 - 4$

$- 3x = - 2 \: | \times ( - 1)$

$3x = 2$

$x = \frac{2}{3}\:\in\:\mathbb{R}$

$4)x - 1 + 2(x - 2) = 3$

$x - 1 + 2x - 4 = 3$

$x + 2x = 3 + 1 + 4$

$3x = 8$

$x = \frac{8}{3}\:\in\:\mathbb{R}$