Solve the equation. What is the value of v?

Question

One way you can start solving is to make sure there are only v terms on one side. What move can you make to both sides of the equation to get rid of the
4
3
​
v on the left, while keeping the equation balanced?
4
3
​
v + 8
=
v + 12

Multiply both sides by
4
3
​
v

Add
4
3
​
v to both
sides

Subtract
4
3
​
v from both
sides

Divide both sides by
4
3
​
v
Nice!
You can subtract
4
3
​
v from the left side of the equation, so that the v terms are only on the right side of the equation, while keeping the equation balanced. Record subtracting
4
3
​
v from both sides now.
4
3
​
v + 8
=
v + 12
−

4
3
​
v
−

4
3
​
v
Great job!
We have v terms on both sides of the equation, and we want to get the v terms on one side. We can subtract
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

=
Great job!
Keep going. Let's try to get
4
1
​
v alone on the right side. How could you get rid of the 12 on the right side so that
4
1
​
v is alone on the right, while keeping the equation balanced?
4
3
​
v + 8
=
v + 12
−
4
3
​
v
−
4
3
​
v

8
=
4
1
​
v + 12

Divide both sides by 12

Add 12 to both sides

Subtract 12 from both sides
Good work!
You can subtract 12 from both sides of the equation to get rid of the 12 on the right, so that
4
1
​
v is alone on the right side of the equation. Record subtracting 12 from both sides now.
4
3
​
v + 8
=
v + 12
−
4
3
​
v
−
4
3
​
v

8
=
4
1
​
v + 12
−

12
−

12
You got it!
Subtract 12 from both sides of the equation to get rid of the 12 on the right, so that
4
1
​
v is alone on the right side of the equation.
4
3
​
v + 8
=
v + 12
−
4
3
​
v
−
4
3
​
v

8
=
4
1
​
v + 12
−
12
−
12

=

Answer 1

Let's solve the equation together step by step!

We started with the equation:

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

Step 1: 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: \[ 8 = v - \frac{4}{3} v + 12 \]

Step 2: Combine the \(v\) terms on the right side.

We can consider \(v\) as \(\frac{3}{3} v\): \[ 8 = \left(\frac{3}{3} - \frac{4}{3}\right)v + 12 = -\frac{1}{3} v + 12 \]

Step 3: Subtract 12 from both sides to isolate the \(-\frac{1}{3} v\) term.

\[ 8 - 12 = -\frac{1}{3} v \] \[ -4 = -\frac{1}{3} v \]

Step 4: Multiply both sides by -3 to solve for \(v\).

\[ -3 \times -4 = v \] \[ 12 = v \]

Thus, the value of \(v\) is: \[ \boxed{12} \]