Question

Ma puteți ajuta cu aceste trei exerciții ?50 puncte

Answer 1

Explicație pas cu pas:

99.

$|2x - 7| \geqslant 5$

$2x - 7 \leqslant - 5 \iff 2x \leqslant 2 \\ \implies x \leqslant 1$

$2x - 7 \geqslant 5 \iff 2x \geqslant 12 \\ \implies x \geqslant 6$

$\implies A = \Big(-\infty ; 1\Big] \cup \Big[6 ; +\infty \Big)$

$|2x - 5| \geqslant 9$

$2x - 5 \leqslant - 9 \iff 2x \leqslant - 4 \\ \implies x \leqslant - 2$

$2x - 5 \geqslant 9 \iff 2x \geqslant 14 \\ \implies x \geqslant 7$

$\implies B = \Big(-\infty ; -2\Big] \cup \Big[7 ; +\infty \Big)$

$A \cup B = \Big(-\infty ; 1\Big] \cup \Big[6 ; +\infty \Big) = A$

$A \cap B = \Big(-\infty ; -2\Big] \cup \Big[7 ; +\infty \Big) = B$

$A - B = \Big( - 2 ; 1\Big] \cup \Big[6 ; 7\Big)$

$B - A = \O$