Question

Scrieti ca interval multimile:
a) A={x apartine R| |x|≤5}
b) B={x apartine R| |x|-1<7}
c) C={x apartine R| |x-5|<1}
d) D={x apartine R| |2x-3|≤11}
​

Answer 1

Explicație pas cu pas:

a)

$|x| \leqslant 5 \\ - 5 \leqslant x \leqslant 5$

=> A = [-5 ; 5]

b)

$|x|-1<7 \\ |x| < 8 \\ - 8 < x < 8$

=> B = (-8 ; 8)

c)

$|x-5|<1 \\ - 1 < x - 5 < 1 \\ 4 < x < 6$

=> C = (4 ; 6)

d)

$|2x-3| \leqslant 11 \\ - 11 \leqslant 2x - 3 \leqslant 11 \\ - 8 \leqslant 2x \leqslant 14 \\ - 4 \leqslant x \leqslant 7$

=> D = [-4 ; 7]