Pregunta
\( \left. \begin{array} { l } { 5 x - 2 > 8 x - 14 } \\ \hline x > - 1 \\ \hline x < 1 \\ \hline x < 4 \\ { O x > 4 } \end{array} \right. \)
Ask by Lewis Weber. in Japan
Jan 24,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
The solution to the inequality is \( x < 4 \).
Solución
Let's solve the inequality step by step:
\[
5x - 2 > 8x - 14
\]
1. **Subtract \(5x\) from both sides:**
\[
-2 > 3x - 14
\]
2. **Add \(14\) to both sides:**
\[
12 > 3x
\]
3. **Divide both sides by \(3\):**
\[
4 > x \quad \text{or} \quad x < 4
\]
So, the solution to the inequality is:
\[
x < 4
\]
**Among the given options:**
- \(x > -1\) ❌
- \(x < 1\) ❌
- \(x < 4\) ✅
- \(x > 4\) ❌
**Final Answer:**
\[
\boxed{x < 4}
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
Como
error msg
Explicar 
Simplifique esta solución Mind Expander
Did you know that inequalities like these were a major breakthrough in mathematics, allowing for the representation of a range of values instead of just a single answer? This concept dates back to ancient civilizations, but it became formally recognized in the 19th century, paving the way for advanced algebra and calculus! When you're solving inequalities, it's a common mistake to forget to flip the inequality sign when multiplying or dividing by a negative number. So remember, if you ever find yourself with something like \(-x > 4\), multiplying both sides by \(-1\) will flip that sign, giving you \(x < -4\). Keep an eye out for those sign changes!
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium
