Question

Solve the equation below. What's the value of r?
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 \( 1 \).