N.5 Graph solutions to one-step inequalities

Question

TMX
Solve the inequality and graph the solution.
p
2
>4
To draw a ray, plot an endpoint and select an arrow. Select an endpoint to change it from closed to open. Select the middle of the ray to delete it.

Answer 1

To solve the inequality \( p + 2 > 4 \), follow these steps:

Step 1: Solve the Inequality

1. Subtract 2 from both sides: \[ p + 2 - 2 > 4 - 2 \] \[ p > 2 \]

Step 2: Graph the Solution

1. Identify the solution: The solution \( p > 2 \) means that \( p \) can take any value greater than 2.

2. Draw the graph:

   • Start by plotting an open circle on 2 (it’s open because 2 is not included in the solution).
   • Draw a ray extending to the right from the open circle to indicate all values greater than 2.

Final Representation

On a number line, it looks like this:

<---|----|-----|-----|----|----|----|----|--->
    0    1     2     3    4    5    6    7
                 ( )
                  --->

Here, the open circle at 2 indicates that 2 is not included in the solution set, and the arrow extending to the right shows that all numbers greater than 2 are included in the solution.