Solve the equation below. What's the value of v?

Question

There are many ways you could solve this equation. We need to get v alone on one side, and a constant number alone on the other side. Since v is inside the parentheses on the left, we can use the distributive property to rewrite the equation without parentheses. Go for it. Distribute the
2
1
​
to 12v−8. You can think of this as (12v−8) is being multiplied by
2
1
​
.
2
1
​
(12v − 8) = 8v + 10
= 8v + 10

Answer 1

Let's start by rewriting the equation you provided and distributing \(\frac{2}{1}\) (which is simply 2) to the expression \(12v - 8\):

\[ 2(12v - 8) = 8v + 10 \]

Now, distribute the 2:

\[ 2 \cdot 12v - 2 \cdot 8 = 8v + 10 \]

This gives us:

\[ 24v - 16 = 8v + 10 \]

Next, let's isolate \(v\) by getting all terms involving \(v\) on one side and constant terms on the other side. Start by subtracting \(8v\) from both sides:

\[ 24v - 8v - 16 = 10 \]

This simplifies to:

\[ 16v - 16 = 10 \]

Now, add 16 to both sides:

\[ 16v = 10 + 16 \]

This simplifies to:

\[ 16v = 26 \]

Lastly, divide both sides by 16 to solve for \(v\):

\[ v = \frac{26}{16} \]

This simplifies to:

\[ v = \frac{13}{8} \]

Therefore, the value of \(v\) is:

\[ \boxed{\frac{13}{8}} \]