Question

Rezolvati in multimea numerelor intregi ecuatiile: a) |x| = 5; b) |x| = -1; c ) | 2x -1| = 7; d) |-x+2| = | -5|

Answer 1

$a)|x|=5\Rightarrow x\in\{-5;5\} \\\\ b)|x|=-1\Rightarrow x\in \emptyset\\Justificare:\ |a|\ \textgreater \ 0\ (\forall) \ a\in\mathbb{R} \\ \\c)|2x-1|=7\\Cazul\ 1:2x-1=7\Rightarrow x=4 \\ Cazul\ 2: 2x-1=-7\Rightarrow x=-3 \\ x\in\{-3;4\} \\ \\d)|-x+2|=|-5|\Leftrightarrow \\ |-x+2|=5 \\ Cazul\ 1:-x+2=5\Rightarrow x=-3 \\ Cazul\ 2:-x+2=-5\Rightarrow x=7 \\ x\in\{-3;7\}$