Question

Rezolvati in multimea numerelor reale inecuatiile:
a) |x| ≤ 3;
b) |x-1|≤4;
c) |4-2x|<8;
d) |x| >6.

Answer 1

$\displaystyle a). |x| \leq 3 \\ x \leq 3 \\ x \geq -3 \\ -3 \leq x \leq 3 \\ x \in [-3,3] \\ b).|x-1| \leq 4 \\ x-1 \leq 4 \\ x \leq 4+1 \\ x \leq 5 \\ x-1 \geq -4 \\ x \geq -4+1 \\ x \geq -3 \\ -3 \leq x \leq 5 \\ x \in [-3,5]$
$c).|4-2x|\ \textless \ 8 \\ 4-2x\ \textless \ 8 \\ -2x\ \textless \ 8-4 \\ -2x\ \textless \ 4 \\ x\ \textgreater \ -2 \\ 4-2x\ \textgreater \ -8 \\ -2x\ \textgreater \ -8-4 \\ -2x\ \textgreater \ -12 \\ x\ \textless \ 6 \\ -2\ \textless \ x\ \textless \ 6 \\ x \in (-2,6)$
$d).|x|\ \textgreater \ 6 \\ x\ \textgreater \ 6 \\ x\ \textless \ -6 \\ x \in ( - \infty , -6) \cup (6 , \infty )$