Question
Solve for \( v \) \[ -12 v-9+7 v=26 \] Simplify your answer as much as possible.
Ask by Zimmerman John. in the United States
Jan 21,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( v = -7 \)
Solution
To solve for \( v \) in the equation:
\[
-12v - 9 + 7v = 26
\]
**Step 1: Combine like terms**
Combine the terms that contain \( v \):
\[
-12v + 7v = -5v
\]
So, the equation becomes:
\[
-5v - 9 = 26
\]
**Step 2: Isolate the term with \( v \)**
Add 9 to both sides of the equation to move the constant term to the right side:
\[
-5v - 9 + 9 = 26 + 9
\]
\[
-5v = 35
\]
**Step 3: Solve for \( v \)**
Divide both sides by \(-5\) to isolate \( v \):
\[
v = \frac{35}{-5}
\]
\[
v = -7
\]
**Final Answer:**
\[
v = -7
\]
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Simplify this solution Extra Insights
To solve for \( v \) in the equation \( -12v - 9 + 7v = 26 \), we first combine like terms on the left side. Combine \( -12v \) and \( 7v \): \[ -12v + 7v = -5v \] So the equation simplifies to: \[ -5v - 9 = 26 \] Next, we isolate \( -5v \) by adding 9 to both sides: \[ -5v = 26 + 9 \] \[ -5v = 35 \] Now, divide both sides by -5 to solve for \( v \): \[ v = \frac{35}{-5} \] \[ v = -7 \] Thus, the solution is: \[ v = -7 \]
