Pregunta
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\( x \) is between \(-4\) and \(-3\).
Solución
To solve the inequality:
\[
3|2x + 7| - 7 < -4
\]
**Step 1: Isolate the Absolute Value**
Add 7 to both sides:
\[
3|2x + 7| < 3
\]
Divide both sides by 3:
\[
|2x + 7| < 1
\]
**Step 2: Remove the Absolute Value**
The inequality \(|2x + 7| < 1\) implies:
\[
-1 < 2x + 7 < 1
\]
**Step 3: Solve for \(x\)**
Subtract 7 from all parts:
\[
-8 < 2x < -6
\]
Divide by 2:
\[
-4 < x < -3
\]
**Solution:**
\( x \) is greater than \(-4\) and less than \(-3\). In interval notation, this is:
\[
(-4,\ -3)
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución Beyond the Answer
First, we start by isolating the absolute value expression in the inequality: \[ 3|2x + 7| - 7 < -4 \] Adding 7 to both sides gives us: \[ 3|2x + 7| < 3 \] Dividing both sides by 3: \[ |2x + 7| < 1 \] Now, we'll break this down into two separate inequalities: 1. \( 2x + 7 < 1 \) 2. \( 2x + 7 > -1 \) Solving the first inequality: \[ 2x < 1 - 7 \] \[ 2x < -6 \] \[ x < -3 \] Now solving the second inequality: \[ 2x > -1 - 7 \] \[ 2x > -8 \] \[ x > -4 \] Finally, combining the two results, we get: \[ -4 < x < -3 \] So, the solution to the inequality \( 3|2x + 7| - 7 < -4 \) is: \[ (-4, -3) \]
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