Question
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Tutor-Verified Answer
Answer
La solución es \( x = -1 \).
Solution
**Paso 1. Expandir ambos lados de la ecuación**
Dada la ecuación:
\[
6(3x-1)-2x=2(2x-5)-8
\]
Expande el lado izquierdo:
\[
6(3x-1)=18x-6
\]
Por tanto, el lado izquierdo se convierte en:
\[
18x-6-2x=16x-6
\]
Expande el lado derecho:
\[
2(2x-5)=4x-10
\]
Después resta 8:
\[
4x-10-8=4x-18
\]
La ecuación se simplifica a:
\[
16x-6=4x-18
\]
---
**Paso 2. Resolver para \( x \)**
Resta \( 4x \) de ambos lados:
\[
16x-6-4x=4x-18-4x
\]
\[
12x-6=-18
\]
Suma 6 a ambos lados:
\[
12x-6+6=-18+6
\]
\[
12x=-12
\]
Divide ambos lados entre 12:
\[
x = \frac{-12}{12}=-1
\]
---
**Respuesta:** \( x=-1 \)
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Simplify this solution Beyond the Answer
To solve the equation, first simplify both sides. Distributing gives: \( 18x - 6 - 2x = 4x - 10 - 8 \). Next, combine like terms: \( 16x - 6 = 4x - 18 \). Then, isolate \( x \) by moving everything involving \( x \) to one side and constant terms to the other: \( 16x - 4x = -18 + 6 \) This simplifies to \( 12x = -12 \). Now, divide by 12 to find \( x \): \( x = -1 \). Solution: \( x = -1 \).
