Solve the inequality and graph the solution.

Question

1>f–7
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of the segment, ray, or line to delete it.

Answer 1

To solve the inequality \( 1 > f - 7 \), we can first rearrange it:

\[ 1 + 7 > f \] \[ 8 > f \] or alternatively, \[ f < 8 \]

This means that \( f \) can take any value less than 8.

Graphing the Solution

1. Endpoints: The endpoint of our solution is \( f = 8 \).
2. Closed or Open: Since \( f \) must be less than 8 and not equal to it, we use an open circle at \( f = 8 \) to indicate that 8 is not included in the solution.
3. Deleting the middle: Since \( f < 8 \) means all numbers less than 8, we will graph this on a number line.

Graph Representation:

• Draw a number line.
• Place an open circle at \( 8 \) to show that it's not included.
• Shade to the left of \( 8 \) to represent all values less than 8.

<---o=========================>
    8

Here, "o" indicates an open circle at \( 8 \) and the line shaded to the left shows all numbers that satisfy the inequality \( f < 8 \).