Question
24. Select all the given values of \( z \) that make the inequality \( 4 z>17 \) true.
Ask by Bowen Daniel. in the United States
Jan 13,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Los valores de \( z \) que satisfacen la desigualdad \( 4z > 17 \) son todos los números mayores que 4.25.
Solution
Para resolver la desigualdad \( 4z > 17 \), sigue estos pasos:
1. **Divide ambos lados de la desigualdad por 4** para despejar \( z \):
\[
\frac{4z}{4} > \frac{17}{4}
\]
Simplificando:
\[
z > 4.25
\]
2. **Interpretación de la solución**:
La desigualdad \( z > 4.25 \) significa que todos los valores de \( z \) que son **mayores que 4.25** satisfacen la desigualdad original \( 4z > 17 \).
**Conclusión:**
Los valores de \( z \) que hacen verdadera la desigualdad \( 4z > 17 \) son **todos los números mayores que 4.25**.
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Simplify this solution Bonus Knowledge
To solve the inequality \( 4z > 17 \), we first need to isolate \( z \). We can do this by dividing both sides of the inequality by 4. This gives us: \[ z > \frac{17}{4} \] Calculating \( \frac{17}{4} \) yields \( 4.25 \). Therefore, any value of \( z \) that is greater than \( 4.25 \) will satisfy the inequality. For example, if we select values like \( 5, 6, \) or \( 10 \), they all satisfy \( z > 4.25 \). However, any value less than or equal to \( 4.25 \), like \( 4 \) or \( 4.25 \) itself, will not satisfy the inequality. So, the complete solution set includes all real numbers greater than \( 4.25 \).
