N.5 Graph solutions to one-step inequalities

Question

TMX
Solve the inequality and graph the solution.
2q≥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 \(2q \geq 4\), follow these steps:

1. Isolate the variable \(q\): \[ 2q \geq 4 \] Divide both sides by 2: \[ q \geq 2 \]

So the solution is \(q \geq 2\).

2. Graph the solution:
   • Plot the point: Place a closed dot (or filled circle) on the number line at \(q = 2\) to indicate that 2 is included in the solution set.
   • Draw the ray: From the point 2, draw a ray that extends to the right (toward larger numbers) to indicate all numbers greater than 2 are included in the solution.

Graph Summary:

• A closed dot on 2 indicates that it is included (since it’s \( \geq \)).
• A solid line or arrow extending to the right shows that all values greater than 2 are part of the solution.

If you're working with tools to graph the inequality:

• Choose the option to plot a closed endpoint at 2.
• Then choose the arrow option to extend the ray to the right.

This visually represents the solution \(q \geq 2\).