Question

We can subtract 10 from both sides to get rid of 10, so that 3r is alone on the right side of the equation. Record subtracting 10 from each side.
4
1
​
(12r−8)
=
6r+10

3r − 2
=
6r + 10
−
3r
−
3r

−2
=
3r +10
−

−

Answer 1

Let's start with the original equation you provided:

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

To simplify and isolate the variable \( r \), we will proceed step by step.

### Step 1: Distribute on the left side

First, distribute \( 4 \) on the left side:

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

### Step 2: Subtract \( 6r \) from both sides

Next, subtract \( 6r \) from both sides to bring the \( r \) terms together:

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

This simplifies to:

\[ 42r - 32 = 10 \]

### Step 3: Add \( 32 \) to both sides

Now, let's add \( 32 \) to both sides to isolate the term with \( r \):

\[ 42r - 32 + 32 = 10 + 32 \]

This simplifies to:

\[ 42r = 42 \]

### Step 4: Divide by \( 42 \)

Finally, divide both sides by \( 42 \) to solve for \( r \):

\[ r = 1 \]

### Summary

To summarize, through a series of steps, we started with the equation:

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

And after performing the appropriate operations, we found:

\[ r = 1 \]