N.5 Graph solutions to one-step inequalities

Question

TMX
Solve the inequality and graph the solution.
3z>6
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 \(3z > 6\), follow these steps:

1. Isolate the variable \(z\): \[ z > \frac{6}{3} \] \[ z > 2 \]

2. Graph the solution:

   • Since \(z\) is greater than 2 (not including 2), you will use an open circle at 2 to indicate that 2 is not part of the solution.
   • Draw a ray starting from 2 and extending to the right, indicating all numbers greater than 2.

Graph:

• On a number line:
  • Mark an open circle at 2.
  • Draw an arrow to the right of the open circle indicating that the solution includes all numbers greater than 2.

This visually represents the solution to the inequality \(z > 2\).