Question

Solve the inequality and graph the solution.
54<58–y

Answer 1

To solve the inequality \( 54 < 58 - y \), follow these steps:

1. **Isolate \( y \)**:
Start by subtracting 58 from both sides:

\[
54 - 58 < -y
\]

Simplifying the left side gives:

\[
-4 < -y
\]

2. **Multiply by -1**:
When you multiply or divide both sides of an inequality by a negative number, the direction of the inequality sign changes:

\[
4 > y
\]

This can be rewritten as:

\[
y < 4
\]

3. **Solution**:
The solution to the inequality is \( y < 4 \).

### Graphing the Solution

To graph \( y < 4 \):

- Draw a number line.
- Mark the point \( 4 \) on the number line.
- Since \( y < 4 \) excludes 4, draw an open circle at \( 4 \) (indicating that 4 is not included in the solution).
- Shade the line to the left of 4, indicating that all values less than 4 are included in the solution.

The final visual representation on the number line would look something like this:

```
<---|---|---|---|---|---|---|---|---|---|-->
-5 -4 -3 -2 -1 0 1 2 3 4
o-----------------
```

Where the open circle at 4 indicates that 4 is not included in the solution.