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La solución es \( x = -10 \).
Solution
Claro, resolveremos la ecuación paso a paso en español.
**Ecuación dada:**
\[ 3x - 8 - 8x = 42 \]
**Paso 1: Simplificar términos semejantes en el lado izquierdo de la ecuación.**
Combina los términos que contienen \( x \):
\[ 3x - 8x = -5x \]
Ahora, la ecuación se simplifica a:
\[ -5x - 8 = 42 \]
**Paso 2: Aislar el término que contiene \( x \).**
Añade 8 a ambos lados de la ecuación para eliminar el término constante del lado izquierdo:
\[
-5x - 8 + 8 = 42 + 8 \\
-5x = 50
\]
**Paso 3: Resolver para \( x \).**
Divide ambos lados de la ecuación por -5 para despejar \( x \):
\[
x = \frac{50}{-5} \\
x = -10
\]
**Resultado:**
\[ x = -10 \]
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Simplify this solution Extra Insights
Let’s simplify the equation first! Combine the terms on the left side: \(3x - 8x = -5x\). So now you have \(-5x - 8 = 42\). Next, add 8 to both sides, giving you \(-5x = 50\). Finally, divide by -5 to isolate \(x\), which gives you \(x = -10\). Voila! You've found your solution! Now that you’ve solved for \(x\), think of how equations like this pop up everywhere in real life! From calculating costs in budgeting, to figuring out distances in travel plans, algebra helps you make sense of the world. So, next time you're balancing your expenses, remember: it's just a math equation waiting to be solved!
