Question

scrisa sub forma de interval multimea A={ apartine R| |2x-1|<5}

Answer 1

$|2x - 1| < 5 \\ = > 2x - 1 < 5 \\ = > - (2x - 1) < 5$
Luam cele 2 cazuri:
$2x - 1 < 5 \\ 2x < 6 \\ x < 3$
$- (2x - 1) < 5 \\ 2x - 1 > - 5 \\ 2x > - 4 \\ x > - 2$
Si acum faci folosind cele 2 inegalitati faci intervalul:
x apartine ( -2 ; 3 )

Answer 2

|x|<a unde a>0 este ⇔-a<x<a
deci
-5<2x-1<5 | adunam 1

-4<2x<6 |impartim cu numarul pozitv 2; inegalitatea pastreaza sensul
-2<x<3⇔x∈(-2;3)
as simple as that!!!