Question

Determinati numerele intregi negative mai mari decat -5 care verifica egalitatiile :
a)3x-2(mai mare sau egal)5x-4
b) |x+1|(mai mic sau egal)4

Answer 1

a)
$3x-2\geq5x-4 \\ \\ 3x+2\geq5x \\ \\ 2\geq2x \\ \\ 2x\leq2 \\ \\ x\leq1 \\ \\ x\in\mathbb{Z}_-\Rightarrow x\in\{-1,-2,-3,-4\}$
b)
$|x+1|\leq4 \\ \\ -4\leq x+1\leq4 \\ \\ -5\leq x\leq3 \\ \\ x\in\mathbb{Z}_-\Rightarrow x\in\{-4,-3,-2,-1\}$