Solve the inequality and graph the solution.

Question

2>
m–3
–
3
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 \( 2 > m - 3 \), we first rewrite it in standard form:

1. Add 3 to both sides: \[ 2 + 3 > m \] which simplifies to: \[ 5 > m \] or equivalently, \[ m < 5 \]

To graph the solution \( m < 5 \):

1. Endpoint: The endpoint in this inequality is \( m = 5 \). Since this is a strict inequality (less than, not less than or equal to), we will use an open circle at this point to indicate that \( m = 5 \) is not included in the solution.

2. Graph: Shade the area to the left of the open circle to represent all values of \( m \) that are less than 5.

Step-by-step graphing:

• Draw a number line.
• Place an open circle on the point 5 (indicating that 5 is not included in the solution).
• Shade all the numbers to the left of the open circle (this represents all values of \( m \) that are less than 5).

Thus, the final graph will look like this:

<---(----|---|---|---|---|---|---|---|---|---|---|---|---|---|--->
       -3  -2  -1   0   1   2   3   4   5   6   7   8   9   10

• The open circle at 5 indicates that 5 is not included in the solution, and the shaded area to the left represents that all values less than 5 are part of the solution set.