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The solution is all real numbers \( x \) where \( 0 < x < 8 \).
Solución
To solve the inequality:
\[
-5|x - 4| > -20
\]
**Step 1: Isolate the Absolute Value**
First, divide both sides of the inequality by **-5**. Remember that when you divide or multiply both sides of an inequality by a negative number, you must **reverse the inequality sign**.
\[
|x - 4| < \frac{-20}{-5}
\]
\[
|x - 4| < 4
\]
**Step 2: Remove the Absolute Value**
The inequality \( |x - 4| < 4 \) means that the expression inside the absolute value, \( x - 4 \), is between -4 and 4.
\[
-4 < x - 4 < 4
\]
**Step 3: Solve for \( x \)**
Add 4 to all parts of the inequality to isolate \( x \):
\[
-4 + 4 < x < 4 + 4
\]
\[
0 < x < 8
\]
**Conclusion**
The solution to the inequality is all real numbers \( x \) such that \( x \) is greater than 0 and less than 8.
**Answer:**
All real numbers x with x between 0 and 8. In other words, the solution is 0 < x < 8.
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución Bonus Knowledge
To solve the inequality \( -5|x-4| > -20 \), we can start by dividing both sides by -5. Remember, when dividing or multiplying both sides of an inequality by a negative number, the inequality sign flips: \[ |x-4| < 4 \] This means the expression inside the absolute value, \(x-4\), must be less than 4 and greater than -4: \[ -4 < x - 4 < 4 \] Now, we can add 4 to all parts of the inequality: \[ 0 < x < 8 \] So, the solution to the inequality is: \[ x \in (0, 8) \]
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