Question
Resolver para \( w \) \[ 3(w+3)=-3(4 w-7)+7 w \] Simplificar la respuesta al máximo. \( w=\square \)
Ask by Cross Craig. in Ecuador
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( w = \frac{3}{2} \)
Solution
Solve the equation \( 3(w+3)=-3(4w-7)+7w \).
Solve the equation by following steps:
- step0: Solve for \(w\):
\(3\left(w+3\right)=-3\left(4w-7\right)+7w\)
- step1: Calculate:
\(3w+9=-3\left(4w-7\right)+7w\)
- step2: Calculate:
\(3w+9=-5w+21\)
- step3: Move the expression to the left side:
\(3w+9-\left(-5w+21\right)=0\)
- step4: Calculate:
\(8w-12=0\)
- step5: Move the constant to the right side:
\(8w=0+12\)
- step6: Remove 0:
\(8w=12\)
- step7: Divide both sides:
\(\frac{8w}{8}=\frac{12}{8}\)
- step8: Divide the numbers:
\(w=\frac{3}{2}\)
La solución para \( w \) en la ecuación dada es \( w = \frac{3}{2} \) o \( w = 1.5 \).
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Simplify this solution The Deep Dive
Para resolver la ecuación \( 3(w+3)=-3(4 w-7)+7 w \), primero distribuimos ambos lados: A la izquierda: \[ 3w + 9 \] A la derecha: \[ -12w + 21 + 7w = -5w + 21 \] Entonces, la ecuación se convierte en: \[ 3w + 9 = -5w + 21 \] Ahora, sumamos \( 5w \) a ambos lados: \[ 3w + 5w + 9 = 21 \] \[ 8w + 9 = 21 \] Restamos 9 de ambos lados: \[ 8w = 12 \] Finalmente, dividimos entre 8: \[ w = \frac{12}{8} = \frac{3}{2} \] Así que la solución simplificada es: \[ w = \frac{3}{2} \]
