Question

xer |x-1|<2
|X+2|<1
|x-5|<3
|2x-1|<1
|2x-5|<3
​

Answer 1

$|x - 1| < 2 \\ - 2 < x - 1 < 2 | +1 \\ - 1 < x < 3$

x€(-1;3)

$|x + 2| < 1 \\ - 1 < x + 2 < 1 | - 2 \\ - 3 < x < - 1$

x€(-3;-1)

$|x - 5| < 3 \\ - 3 < x - 5 < 3 | + 5 \\ 2 < x < 8$

x€(2;8)

$|2x - 1| < 1 \\ - 1 < 2x - 1 < 1 | + 1 \\ 0 < 2x < 2 | \div 2 \\ 0 < x < 1$

x€(0;1)

$|2x - 5| < 3 \\ - 3 < 2x - 5 < 3 | + 5 \\ 2 < 2x < 8 | \div 2 \\ 1 < x < 4$

x€(1;4)

"€" semnul de "aparține"