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Si [tex]$a=2x^2+1$[/tex] y [tex]$b=-3x+5$[/tex], ¿cuál es el valor de [tex][tex]$z=2a-3b-4$[/tex][/tex]?

Sagot :

Claro, resolvamos paso a paso para encontrar el valor de [tex]\( z \)[/tex] dado [tex]\( a = 2x^2 + 1 \)[/tex] y [tex]\( b = -3x + 5 \)[/tex].

Primero, escribamos la expresión para [tex]\( z \)[/tex]:

[tex]\[ z = 2a - 3b - 4 \][/tex]

Ahora, necesitamos sustituir [tex]\( a \)[/tex] y [tex]\( b \)[/tex] en esta expresión.

1. Sustituimos [tex]\( a = 2x^2 + 1 \)[/tex]:

[tex]\[ 2a = 2(2x^2 + 1) = 4x^2 + 2 \][/tex]

2. Sustituimos [tex]\( b = -3x + 5 \)[/tex]:

[tex]\[ -3b = -3(-3x + 5) = 9x - 15 \][/tex]

3. Sumamos los términos obtenidos y restamos 4:

[tex]\[ z = 2a - 3b - 4 = (4x^2 + 2) + (9x - 15) - 4 \][/tex]

Ahora, combinamos todos los términos:

[tex]\[ z = 4x^2 + 9x + 2 - 15 - 4 \][/tex]
[tex]\[ z = 4x^2 + 9x - 17 \][/tex]

Por lo tanto, el valor de [tex]\( z \)[/tex] es:

[tex]\[ z = 4x^2 + 9x - 17 \][/tex]
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