Ensino Médio ⇒ Inequações modulares Tópico resolvido

[Caduzin3445]

Quais os números inteiros que satisfazem a sentença 3=<|2x-3|<6?

Gab: -1,0,3 e 4

[petras]

Caduzin3445,

[tex3]3\leq|2x-3|<6\\
3 \leq |2x-3| \implies |2x-3|\geq3\\
2x-3 \geq 3 \implies x \geq 3 \vee -(2x-3) >3 \implies x \leq 0(I)\\
|2x-3| < 6\\
2x-3 < 6 \implies x < \frac{9}{2} \vee -(2x-3) <6 \implies x>- \frac{3}{2} \implies -\frac{3}{2} < x <3 (II)\\
(I)\cap II): \boxed{-\frac{3}{2} < x\leq 0 \vee3 \leq x < \frac {9}{2}}\\
\therefore \{-1,0,3,4\}

[/tex3]

Código: Selecionar tudoSHIFT+Click na eq = ZOOM

[tex3]3\leq|2x-3|<6\\
3 \leq |2x-3| \implies |2x-3|\geq3\\
2x-3 \geq 3 \implies x \geq 3 \vee -(2x-3) >3 \implies x \leq 0(I)\\
|2x-3| < 6\\
2x-3 < 6 \implies x < \frac{9}{2} \vee -(2x-3) <6 \implies x>- \frac{3}{2} \implies -\frac{3}{2} < x <3 (II)\\
(I)\cap II): \boxed{-\frac{3}{2} < x\leq 0 \vee3 \leq x < \frac {9}{2}}\\
\therefore \{-1,0,3,4\}

[/tex3]