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

Question

There are many ways you could solve this equation. We need to get r alone on one side, and a constant number alone on the other side. Since r is inside the parentheses on the left, we can use the distributive property to rewrite the equation without parentheses. Go for it. Distribute the
4
1
​
to 12r−8. You can think of this as (12r−8) is being multiplied by
4
1
​
.
4
1
​
(12r − 8) = 6r + 10
= 6r + 10

Answer 1

To solve the equation \( \frac{4}{1} (12r - 8) = 6r + 10 \), let's start by distributing the \( \frac{4}{1} \) (which is simply 4) to the terms inside the parentheses:

\[ 4(12r - 8) = 6r + 10 \]

Distributing 4 gives:

\[ 4 \cdot 12r - 4 \cdot 8 = 6r + 10 \]

This simplifies to:

\[ 48r - 32 = 6r + 10 \]

Next, we want to get all the \( r \) terms on one side and the constant terms on the other. First, subtract \( 6r \) from both sides:

\[ 48r - 6r - 32 = 10 \]

This simplifies to:

\[ 42r - 32 = 10 \]

Now, add 32 to both sides:

\[ 42r = 10 + 32 \]

This simplifies to:

\[ 42r = 42 \]

Finally, divide by 42:

\[ r = \frac{42}{42} \]

Thus, we find:

\[ r = 1 \]

The value of \( r \) is \( 1 \).