Solve the inequality and graph the solution.

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.