Question

Solve the equation. Check your solution.
minus8yplus8equals37yminus7

Answer 1

To solve the equation \(-8y + 8 = 37y - 7\), we will first isolate \(y\).

1. **Rearranging the equation**:
\[-8y + 8 = 37y - 7\]
We can move all terms involving \(y\) to one side and the constant terms to the other side. Let's add \(8y\) to both sides and add \(7\) to both sides:
\[
8 + 7 = 37y + 8y
\]
This simplifies to:
\[
15 = 45y
\]

2. **Solving for \(y\)**:
\[
y = \frac{15}{45} = \frac{1}{3}
\]

3. **Checking the solution**:
Substitute \(y = \frac{1}{3}\) back into the original equation:
\[
-8\left(\frac{1}{3}\right) + 8 = 37\left(\frac{1}{3}\right) - 7
\]
Calculate the left side:
\[
-\frac{8}{3} + 8 = -\frac{8}{3} + \frac{24}{3} = \frac{16}{3}
\]
Calculate the right side:
\[
37\left(\frac{1}{3}\right) - 7 = \frac{37}{3} - \frac{21}{3} = \frac{16}{3}
\]

Since both sides are equal, our solution is verified.

Thus, the solution to the equation is:
\[
\boxed{\frac{1}{3}}
\]