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4. Resuelvo las siguientes ecuaciones. \[ \begin{array}{l}\text { a) } 3 x-1-(x-4)-[2(x-3)(1-2)]=x+2\end{array} \]

Ask by Hills Daniels. in Ecuador
Feb 21,2025

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Tutor-Verified Answer

Answer

La solución es \( x = \frac{5}{3} \) o \( x = 1.\dot{6} \).

Solution

Solve the equation \( 3x-1-(x-4)-[2(x-3)(1-2)]=x+2 \). Solve the equation by following steps: - step0: Solve for \(x\): \(3x-1-\left(x-4\right)-\left(2\left(x-3\right)\left(1-2\right)\right)=x+2\) - step1: Simplify: \(2x+3+2\left(x-3\right)=x+2\) - step2: Move the expression to the left side: \(2x+3+2\left(x-3\right)-\left(x+2\right)=0\) - step3: Calculate: \(x+1+2\left(x-3\right)=0\) - step4: Calculate: \(3x-5=0\) - step5: Move the constant to the right side: \(3x=0+5\) - step6: Remove 0: \(3x=5\) - step7: Divide both sides: \(\frac{3x}{3}=\frac{5}{3}\) - step8: Divide the numbers: \(x=\frac{5}{3}\) La solución de la ecuación dada es \( x = \frac{5}{3} \) o \( x = 1.\dot{6} \).

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Para resolver la ecuación \(3x - 1 - (x - 4) - [2(x - 3)(1 - 2)] = x + 2\), primero simplificamos las expresiones dentro de los paréntesis y corchetes. Observamos que \(1 - 2 = -1\), así que podemos reescribir \(2(x - 3)(-1)\) como \(-2(x - 3)\). Esto nos lleva a \(3x - 1 - (x - 4) + 2(x - 3) = x + 2\). Ahora agrupamos los términos: \(3x - 1 - x + 4 - 2(x - 3) = x + 2\). Distribuyendo \(2\) y simplificando, obtenemos \(3x - 1 - x + 4 + 2x - 6 = x + 2\), que se simplifica a \(4x - 3 = x + 2\). Restamos \(x\) de ambos lados y sumamos \(3\), llegando a \(3x = 5\). Por último, dividimos entre \(3\) y hallamos que \(x = \frac{5}{3}\). Ahora, para la parte b, llévanos a la siguiente ecuación y repite el proceso. ¡Tú puedes hacerlo!

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