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5. Si [tex]$x$[/tex] y [tex]$y$[/tex] son números reales, tal que [tex]$|x|\ \textless \ |y|$[/tex], ¿cuál de las siguientes parejas de números hace cierta la desigualdad?

A. [tex][tex]$x=2, y=1$[/tex][/tex]

B. [tex]$x=1, y=2$[/tex]

C. [tex]$x=-3, y=2$[/tex]

D. [tex][tex]$x=0, y=-1$[/tex][/tex]

Sagot :

GinnyAnswer
Para resolver la pregunta, debemos evaluar la desigualdad [tex]\( |x| < |y| \)[/tex] usando la pareja de números proporcionada, que es [tex]\( x = 2 \)[/tex] y [tex]\( y = 1 \)[/tex].

1. Primero, encontramos los valores absolutos de [tex]\( x \)[/tex] y [tex]\( y \)[/tex]:
- El valor absoluto de [tex]\( x \)[/tex] es [tex]\( |x| = |2| = 2 \)[/tex].
- El valor absoluto de [tex]\( y \)[/tex] es [tex]\( |y| = |1| = 1 \)[/tex].

2. Luego, comparamos los valores absolutos obtenidos:
- Queremos saber si [tex]\( |x| < |y| \)[/tex], es decir, si [tex]\( 2 < 1 \)[/tex].

3. Al comparar 2 y 1, vemos que 2 no es menor que 1.

Por lo tanto, para la pareja de números [tex]\( x = 2 \)[/tex] y [tex]\( y = 1 \)[/tex], la desigualdad [tex]\( |x| < |y| \)[/tex] no se cumple.

La respuesta es falsa para la opción A.
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