Questions: Solve for (v). [ -7 v+11 v+5=2 v+31 ] Simplify your answer as much as possible. [ v= ]

Solve for (v). [ -7 v+11 v+5=2 v+31 ] Simplify your answer as much as possible. [ v= ]
Transcript text: Solve for $v$. \[ -7 v+11 v+5=2 v+31 \] Simplify your answer as much as possible. \[ v= \]
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Solution

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Solution Steps

Step 1: Combine Like Terms

First, combine like terms on the left side of the equation: \[ -7v + 11v + 5 = 2v + 31 \] This simplifies to: \[ 4v + 5 = 2v + 31 \]

Step 2: Isolate the Variable

Next, isolate the variable \( v \) by subtracting \( 2v \) from both sides: \[ 4v - 2v + 5 = 31 \] This simplifies to: \[ 2v + 5 = 31 \]

Step 3: Solve for \( v \)

Subtract 5 from both sides to further isolate \( v \): \[ 2v = 26 \] Finally, divide both sides by 2: \[ v = 13 \]

Final Answer

\[ \boxed{v = 13} \]

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