Pregunta
Solución de tutoría real
Respuesta verificada por el tutor
Responder
The solution to the inequality \( 4|m - 5| - 4 < 20 \) is all real numbers \( m \) such that \( -1 < m < 11 \).
Solución
To solve the inequality \( 4|m - 5| - 4 < 20 \), follow these steps:
1. **Isolate the absolute value term:**
\[
4|m - 5| - 4 < 20
\]
Add 4 to both sides:
\[
4|m - 5| < 24
\]
2. **Divide both sides by 4 to simplify:**
\[
|m - 5| < 6
\]
3. **Interpret the absolute value inequality:**
The inequality \( |m - 5| < 6 \) means that the expression inside the absolute value is less than 6 units away from 0. This can be rewritten as a compound inequality:
\[
-6 < m - 5 < 6
\]
4. **Solve for \( m \):**
Add 5 to all parts of the inequality:
\[
-6 + 5 < m < 6 + 5
\]
\[
-1 < m < 11
\]
**Solution:**
All real numbers m with m greater than –1 and less than 11.
In interval notation:
\( -1 < m < 11 \)
Revisado y aprobado por el equipo de tutoría de UpStudy
Como
error msg
Explicar 
Simplifique esta solución Mind Expander
To solve the inequality \( 4|m-5|-4<20 \), we start by isolating the absolute value term. 1. Add 4 to both sides: \[ 4|m-5| < 24 \] 2. Divide both sides by 4: \[ |m-5| < 6 \] Next, we interpret the absolute value inequality \( |m-5| < 6 \), which translates to: \[ -6 < m-5 < 6 \] 3. Now, we solve for \( m \) by adding 5 throughout the inequality: \[ -6 + 5 < m < 6 + 5 \] \[ -1 < m < 11 \] Therefore, the solution to the inequality is: \[ m \in (-1, 11) \]
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium
