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.

Question

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:

\[ r = 1 \]