Pregunta
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\( u = -6 \)
Solución
To solve the equation for \( u \):
\[
2(u + 7) = -6u - 34
\]
**Step 1: Distribute the 2 on the left side**
\[
2 \cdot u + 2 \cdot 7 = -6u - 34 \\
2u + 14 = -6u - 34
\]
**Step 2: Move all terms containing \( u \) to one side and constant terms to the other**
Add \( 6u \) to both sides:
\[
2u + 6u + 14 = -6u + 6u - 34 \\
8u + 14 = -34
\]
**Step 3: Isolate the term with \( u \)**
Subtract \( 14 \) from both sides:
\[
8u + 14 - 14 = -34 - 14 \\
8u = -48
\]
**Step 4: Solve for \( u \)**
Divide both sides by \( 8 \):
\[
u = \frac{-48}{8} \\
u = -6
\]
**Solution:**
\[
u = -6
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución The Deep Dive
To solve for \( u \) in the equation \( 2(u+7)=-6u-34 \), let's start by distributing on the left side: \[ 2u + 14 = -6u - 34 \] Next, we'll add \( 6u \) to both sides to get all terms involving \( u \) on one side: \[ 2u + 6u + 14 = -34 \] This simplifies to: \[ 8u + 14 = -34 \] Now, we will subtract 14 from both sides: \[ 8u = -34 - 14 \] \[ 8u = -48 \] Finally, divide both sides by 8 to solve for \( u \): \[ u = \frac{-48}{8} = -6 \] So, the solution is: \[ u = -6 \]
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