Question

Solve the equation below. What's the value of v?
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
5
1
​
to 15v−10. You can think of this as (15v−10) is being multiplied by
5
1
​
.
5
1
​
(15v − 10) = 8v + 8
= 8v + 8

Answer 1

To solve the equation \( 5(15v - 10) = 8v + 8 \), we will first use the distributive property to eliminate the parentheses on the left side of the equation.

### Step 1: Distribute the 5
\[
5(15v - 10) = 5 \cdot 15v - 5 \cdot 10
\]
This simplifies to:
\[
75v - 50
\]

### Step 2: Rewrite the equation
Now the equation can be rewritten as:
\[
75v - 50 = 8v + 8
\]

### Step 3: Get all \( v \) terms on one side and constant terms on the other side
Subtract \( 8v \) from both sides:
\[
75v - 8v - 50 = 8
\]
This simplifies to:
\[
67v - 50 = 8
\]

Next, add 50 to both sides:
\[
67v = 8 + 50
\]
This simplifies to:
\[
67v = 58
\]

### Step 4: Solve for \( v \)
Now, divide both sides by 67:
\[
v = \frac{58}{67}
\]

Thus, the value of \( v \) is:
\[
\boxed{\frac{58}{67}}
\]