Question

How many solutions does this equation have?
-15r + 12 = 3(-15r + 4)

Answer 1

To determine how many solutions the equation \(-15r + 12 = 3(-15r + 4)\) has, we can start by simplifying the equation.

First, distribute the \(3\) on the right side:

\[
3(-15r + 4) = 3 \cdot -15r + 3 \cdot 4 = -45r + 12
\]

Now, rewrite the original equation with this simplification:

\[
-15r + 12 = -45r + 12
\]

Next, let's isolate the terms involving \(r\). To do this, we can add \(45r\) to both sides:

\[
-15r + 45r + 12 = 12
\]

This simplifies to:

\[
30r + 12 = 12
\]

Now, we will subtract \(12\) from both sides:

\[
30r = 0
\]

Next, divide both sides by \(30\):

\[
r = 0
\]

Since we found a specific value for \(r\), this means there is exactly one solution to the equation.

Thus, the number of solutions is \( \boxed{1} \).