Questions: 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. \[ v= \]

Solution

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: \[ v = 13 \]

\[ \boxed{v = 13} \]

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