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Simplify the expression: [tex]\(12x - 2[4x - 7(x - 2) + 3]\)[/tex]

A. [tex]\(18x - 31\)[/tex]
B. [tex]\(22 - 10x\)[/tex]
C. [tex]\(7 - 3x\)[/tex]
D. [tex]\(18x - 34\)[/tex]

Sagot :

GinnyAnswer
Vamos a simplificar la expresión [tex]\(12x - 2[4x - 7(x - 2) + 3]\)[/tex] paso a paso:

1. Distribuir el término -2 dentro del corchete:
Primero trabajemos dentro del corchete:
[tex]\[ 4x - 7(x - 2) + 3 \][/tex]

2. Distribuir el -7 en [tex]\(7(x - 2)\)[/tex]:
[tex]\[ 7(x - 2) = 7x - 14 \][/tex]
Así que la expresión dentro del corchete se convierte en:
[tex]\[ 4x - 7x + 14 + 3 \][/tex]

3. Combinando términos similares dentro del corchete:
[tex]\[ 4x - 7x = -3x \][/tex]
[tex]\[ 14 + 3 = 17 \][/tex]
Entonces la expresión dentro del corchete ahora es:
[tex]\[ -3x + 17 \][/tex]

4. Multiplicar con el -2:
[tex]\[ -2(-3x + 17) = 6x - 34 \][/tex]

5. Simplificar la expresión completa:
[tex]\[ 12x - (6x - 34) \][/tex]
Esto se convierte en:
[tex]\[ 12x - 6x + 34 = 6x + 34 \][/tex]

Finalmente, combinando todo obtenemos:
[tex]\[ 12x + 6x - 34 = 18x - 34 \][/tex]

Así que la expresión simplificada es [tex]\(18x - 34\)[/tex]. La respuesta correcta es:

D) [tex]\(18x - 34\)[/tex]
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