Question

Solve the equation. Check your solution.
six fifths y minus 2 equals 40
6
5y−2=40

Answer 1

To solve the equation \(\frac{6}{5}y - 2 = 40\), follow these steps:

1. **Add 2 to both sides**:
\[
\frac{6}{5}y - 2 + 2 = 40 + 2
\]
\[
\frac{6}{5}y = 42
\]

2. **Multiply both sides by \(\frac{5}{6}\)** to solve for \(y\):
\[
y = 42 \times \frac{5}{6}
\]

3. **Calculate \(42 \times \frac{5}{6}\)**:
\[
y = \frac{42 \times 5}{6} = \frac{210}{6} = 35
\]

Thus, the solution is \(y = 35\).

### Check the solution

Substitute \(y = 35\) back into the original equation:

\[
\frac{6}{5}(35) - 2 = 40
\]

Calculate \(\frac{6}{5}(35)\):
\[
\frac{6 \times 35}{5} = \frac{210}{5} = 42
\]

Now, substitute back:
\[
42 - 2 = 40
\]

Since this holds true, the solution \(y = 35\) is indeed correct.