We have v terms on both sides of the equation, and we want to get the v terms on one side. We can subtract

Question

4
3
​
v on the left side of the equation so that there are no v terms on the left. Then we need to subtract
4
3
​
v from the right to keep the equation balanced. Go for it.
4
3
​
v + 8
=
v + 12
−
4
3
​
v
−
4
3
​
v

=

Answer 1

Let's solve the equation step by step as per your instructions.

Starting with the original equation:

\[ \frac{4}{3} v + 8 = v + 12 \]

Now, we will subtract \(\frac{4}{3} v\) from both sides:

\[ \frac{4}{3} v + 8 - \frac{4}{3} v = v + 12 - \frac{4}{3} v \]

This simplifies to:

\[ 8 = v + 12 - \frac{4}{3} v \]

Now, to combine the \(v\) terms on the right side, we can rewrite \(v\) as \(\frac{3}{3} v\):

\[ 8 = \frac{3}{3} v + 12 - \frac{4}{3} v \]

Now we can combine the \(v\) terms:

\[ 8 = \frac{3}{3} v - \frac{4}{3} v + 12 \]

\[ 8 = -\frac{1}{3} v + 12 \]

So the equation now is:

\[ 8 = -\frac{1}{3} v + 12 \]

This is the equation after collecting all the \(v\) terms to one side. To solve for \(v\), we can subtract 12 from both sides:

\[ 8 - 12 = -\frac{1}{3} v \]

\[ -4 = -\frac{1}{3} v \]

Now, multiplying both sides by -3 to isolate \(v\):

\[ v = 12 \]

So, the solution for \(v\) is:

\[ \boxed{12} \]