Question
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Answer
La ecuación es verdadera para cualquier valor de \( x \).
Solution
Para resolver la ecuación \( 3 + 3x - 1 = x + 2 + 2x \), primero simplificamos ambos lados.
1. Simplificamos el lado izquierdo:
\[
3 - 1 + 3x = 2 + 3x
\]
2. Simplificamos el lado derecho:
\[
x + 2 + 2x = 3x + 2
\]
Ahora la ecuación se ve así:
\[
2 + 3x = 3x + 2
\]
3. Restamos \( 3x \) de ambos lados:
\[
2 = 2
\]
Esto es una identidad, lo que significa que la ecuación es verdadera para cualquier valor de \( x \). Por lo tanto, la solución es que \( x \) puede ser cualquier número real.
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Simplify this solution Extra Insights
To solve the equation \( 3 + 3x - 1 = x + 2 + 2x \), first, simplify both sides. The left side becomes \( 2 + 3x \), and the right side simplifies to \( 2 + 3x \). Both sides are equal, meaning this equation holds true for all values of \( x \) – it represents a true statement. This means you have an identity, which indicates that any real number can be substituted for \( x \), and the equation will still be valid. Isn't it fascinating when math brings us such universal truths? It’s like finding out a secret that binds everything together!
