Questions: Solve for (v). [ -3 v+2=-10 v+30 ] Simplify your answer as much as possible. [ v= ]

Solve for (v). [ -3 v+2=-10 v+30 ] Simplify your answer as much as possible. [ v= ]
Transcript text: Solve for $v$. \[ -3 v+2=-10 v+30 \] Simplify your answer as much as possible. \[ v= \]
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Solution

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Solution Steps

To solve for \( v \), we need to isolate the variable on one side of the equation. Start by adding \( 10v \) to both sides to get all terms involving \( v \) on one side. Then, simplify the equation by combining like terms. Finally, solve for \( v \) by isolating it.

Step 1: Move Terms Involving \( v \) to One Side

Start with the equation: \[ -3v + 2 = -10v + 30 \] Add \( 10v \) to both sides to get: \[ -3v + 10v + 2 = 30 \]

Step 2: Combine Like Terms

Combine the terms involving \( v \): \[ 7v + 2 = 30 \]

Step 3: Isolate the Variable \( v \)

Subtract 2 from both sides to isolate the term with \( v \): \[ 7v = 28 \]

Step 4: Solve for \( v \)

Divide both sides by 7 to solve for \( v \): \[ v = 4 \]

Final Answer

\(\boxed{v = 4}\)

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