Solve for v =6(v-3)+2v=22   . Simplify your answer as much as possible

Let's solve the equation step by step:

The given equation is:

\[
6(v - 3) + 2v = 22
\]

### Step 1: Distribute the 6 across the terms inside the parentheses.

\[
6v - 18 + 2v = 22
\]

### Step 2: Combine like terms on the left side.

\[
(6v + 2v) - 18 = 22
\]

\[
8v - 18 = 22
\]

### Step 3: Add 18 to both sides to isolate the term with \(v\).

\[
8v = 22 + 18
\]

\[
8v = 40
\]

### Step 4: Divide both sides by 8 to solve for \(v\).

\[
v = \frac{40}{8} = 5
\]

So, the solution is:

\[
v = 5
\]

Would you like any further details or have any questions about the solution?

### Related Questions:
1. What if the equation was \(6(v + 3) + 2v = 22\)?
2. How would you solve the equation if it were \(6(v - 3) + 2v = 30\)?
3. Can you solve for \(v\) if the equation was \(6(v - 3) + 3v = 22\)?
4. What happens if we add a constant on both sides of the equation?
5. How do we solve the equation \(7(v - 2) + 3v = 28\)?
6. What if the original equation had a different constant, say \(6(v - 3) + 2v = 24\)?
7. Can you solve \(5(v - 4) + 4v = 23\)?
8. How does the process change if there's a fraction involved, like \( \frac{v - 3}{2} + 2v = 22\)?

### Tip:
When solving linear equations, always start by simplifying both sides of the equation as much as possible before isolating the variable.

Learn how to solve the equation 6(v - 3) + 2v = 22 step-by-step with detailed explanations. This problem covers key algebraic concepts, including linear equations and variable isolation techniques. Suitable for students in Grades 7-9.

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