Question

1/2y - 9/5≤-1
solve the inequality step by step

Answer 1

To solve the inequality

\[
\frac{1}{2}y - \frac{9}{5} \leq -1,
\]

we can follow these steps:

### Step 1: Isolate the term containing \(y\)

Start by adding \(\frac{9}{5}\) to both sides of the inequality:

\[
\frac{1}{2}y - \frac{9}{5} + \frac{9}{5} \leq -1 + \frac{9}{5}.
\]

This simplifies to:

\[
\frac{1}{2}y \leq -1 + \frac{9}{5}.
\]

### Step 2: Simplify the right side

To simplify \(-1 + \frac{9}{5}\), we can express \(-1\) as \(-\frac{5}{5}\):

\[
-1 + \frac{9}{5} = -\frac{5}{5} + \frac{9}{5} = \frac{4}{5}.
\]

Now, we have:

\[
\frac{1}{2}y \leq \frac{4}{5}.
\]

### Step 3: Solve for \(y\)

To eliminate the fraction \(\frac{1}{2}\), multiply both sides by \(2\):

\[
2 \cdot \frac{1}{2}y \leq 2 \cdot \frac{4}{5}.
\]

This simplifies to:

\[
y \leq \frac{8}{5}.
\]

### Step 4: Write the final answer

The solution to the inequality is:

\[
y \leq \frac{8}{5}.
\]

### Conclusion

Thus, the solution to the inequality \(\frac{1}{2}y - \frac{9}{5} \leq -1\) is

\[
y \leq \frac{8}{5}.
\]