Question

Se -1 < 2x + 3 < 1 entao 2-x está entre:
a. 1 e 3
b.-1 e 0
c. 0 e 1
d. 1 e 2
e. 3 e 4​

Answer 1

$-1 < 2x + 3 < 1 \\\frac{ - 1}{ - 2} < \frac{2x}{ - 2} + \frac{3}{ - 2} < \frac{1}{ - 2} \\ \frac{1}{2} > - x - \frac{3}{2} > - \frac{1}{2}$

$- \frac{1}{2} < - x - \frac{3}{2} < \frac{1}{2} \\ - \frac{1}{2} + \frac{7}{2} < - x - \frac{3}{2} + \frac{7}{2} < \frac{1}{2} + \frac{7}{2}$

$\frac{6}{2} < 2 - x < \frac{8}{2} \\ 3 < 2 - x < 4$

Alternativa e