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
Nice!
You rewrote the left side of the equation without parentheses. Now, we can keep solving by making sure there are only r terms on one side of the equation. Let’s get rid of the r terms on the left so there are only r terms on the right side. What move can you make next to get rid of 3r on the left, while keeping the equation balanced?
4
1
​
(12r−8)
=
6r+10

3r − 2
=
6r + 10

Multiply both sides by 3r

Add 3r to both sides

Subtract 3r from both sides

Divide both sides by 3r
Excellent!
You can subtract 3r from both sides of the equation to get rid of the 3r on the left, so that all the r terms are on the right side of the equation. Record subtracting 3r from both sides now.
4
1
​
(12r−8)
=
6r+10

3r − 2
=
6r + 10
−

3r
−

3r
Great job!
Subtract 3r from both sides of the equation to get rid of the 3r on the left, so that all the r terms are on the right side of the equation.
4
1
​
(12r−8)
=
6r+10

3r − 2
=
6r + 10
−
3r
−
3r

=
You got it!
Now that you have all the variables on the right, you can start thinking about how to make sure all the constant numbers are only on one side. What move can you make to get rid of the 10 on the right, so that 3r is alone on the right side, while keeping the equation balanced?
4
1
​
(12r−8)
=
6r+10

3r − 2
=
6r + 10
−
3r
−
3r

−2
=
3r + 10

Subtract 10 from both sides of the equation

Divide both sides by 10

Add 10 to both sides of the equation
Good work!
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
−

10
−

10
You got it!
Subtract 10 from each side of the equation to get rid of 10 on the right, so that 3r is alone on the right side of the equation.
4
1
​
(12r−8)
=
6r+10

3r − 2
=
6r + 10
−
3r
−
3r

−2
=
3r +10
−
10
−
10

=

Answer 1

Let's solve the equation step by step, following the process you outlined.

Starting with the equation:

\[ \frac{4}{1}(12r - 8) = 6r + 10 \]

Let's simplify the left side using the distributive property:

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

Distributing \(4\):

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

Next, let's move all \(r\) terms to one side. We can subtract \(6r\) from both sides of the equation:

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

This simplifies to:

\[ 42r - 32 = 10 \]

Next, to isolate the \(r\) term, we add \(32\) to both sides:

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

Now, divide both sides by \(42\):

\[ r = \frac{42}{42} \] \[ r = 1 \]

Thus, the value of \(r\) is:

\[ \boxed{1} \]