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
5
1
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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: \[ \boxed{\frac{58}{67}} \]