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z) \( \frac{7 x-6}{3}-(x+2)=4 x+2 \)

Ask by Pollard Griffin. in Mexico
Mar 20,2025

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Answer

La solución de la ecuación es \( x = -\frac{9}{4} \).

Solution

Resolver la ecuación \[ \frac{7x-6}{3}-(x+2)=4x+2 \] **Paso 1:** Multiplicar ambos lados de la ecuación por 3 para eliminar la fracción. Multiplicamos: \[ 3\left(\frac{7x-6}{3}-(x+2)\right)=3(4x+2) \] Simplificando, se obtiene: \[ 7x-6-3(x+2)=12x+6 \] **Paso 2:** Expandir los términos en el lado izquierdo. Distribuir \(-3\) sobre \((x+2)\): \[ 7x-6-3x-6=12x+6 \] Simplificar combinando términos semejantes: \[ (7x-3x)-(6+6)=12x+6 \quad \Rightarrow \quad 4x-12=12x+6 \] **Paso 3:** Aislar el término que contiene \( x \). Restar \( 4x \) de ambos lados: \[ 4x-12-4x=12x+6-4x \quad \Rightarrow \quad -12=8x+6 \] Luego, restar 6 de ambos lados: \[ -12-6=8x+6-6 \quad \Rightarrow \quad -18=8x \] **Paso 4:** Despejar \( x \) dividiendo ambos lados entre 8. \[ x=\frac{-18}{8}=\frac{-9}{4} \] La solución de la ecuación es: \[ x=-\frac{9}{4} \]

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To solve the equation \( \frac{7 x-6}{3}-(x+2)=4 x+2 \), start by eliminating the fraction. Multiply through by 3: \[ 7x - 6 - 3(x + 2) = 12x + 6 \] Distributing gives: \[ 7x - 6 - 3x - 6 = 12x + 6 \] Combine like terms: \[ 4x - 12 = 12x + 6 \] Next, isolate the variable by moving terms involving \( x \) to one side: \[ 4x - 12x = 6 + 12 \] This simplifies to: \[ -8x = 18 \] Now, divide both sides by -8: \[ x = -\frac{9}{4} \] The final solution is \( x = -\frac{9}{4} \). Happy solving!

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