Questions: 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. \[ v= \]

Solution

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 $: \[ v = 4 \]