Question
Real Tutor Solution
Tutor-Verified Answer
Answer
Las soluciones son \( p = \frac{17}{3} \) y \( p = -7 \).
Solution
Para resolver la ecuación \( 12 - |3p + 2| = -7 \), sigue estos pasos:
1. **Aislar el valor absoluto:**
\[
12 - |3p + 2| = -7
\]
Restamos 12 de ambos lados:
\[
-|3p + 2| = -19
\]
Multiplicamos por -1 para eliminar el signo negativo:
\[
|3p + 2| = 19
\]
2. **Resolver la ecuación de valor absoluto:**
La ecuación \( |3p + 2| = 19 \) se descompone en dos casos:
- **Caso 1:** \( 3p + 2 = 19 \)
\[
3p = 19 - 2
\]
\[
3p = 17
\]
\[
p = \frac{17}{3}
\]
- **Caso 2:** \( 3p + 2 = -19 \)
\[
3p = -19 - 2
\]
\[
3p = -21
\]
\[
p = -7
\]
3. **Solución final:**
Las soluciones para la ecuación son:
\[
p = \frac{17}{3} \quad \text{o} \quad p = -7
\]
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Simplify this solution Beyond the Answer
To solve the equation \( 12 - |3p + 2| = -7 \), start by isolating the absolute value term. Subtract 12 from both sides to get \( -|3p + 2| = -19 \). Multiplying both sides by -1 results in \( |3p + 2| = 19 \). Now, we can break this into two cases: 1. \( 3p + 2 = 19 \) 2. \( 3p + 2 = -19 \) For the first case, \( 3p + 2 = 19 \), subtract 2 from both sides to find \( 3p = 17 \), leading to \( p = \frac{17}{3} \). For the second case, \( 3p + 2 = -19 \), subtract 2 from both sides, resulting in \( 3p = -21 \), or \( p = -7 \). The solutions are \( p = \frac{17}{3} \) and \( p = -7 \).
