N.5 Graph solutions to one-step inequalities

Question

TMX
Solve the inequality and graph the solution.
m+6≥10
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 \( m + 6 \geq 10 \), follow these steps:

1. Subtract 6 from both sides to isolate \( m \): \[ m + 6 - 6 \geq 10 - 6 \] This simplifies to: \[ m \geq 4 \]

2. Graph the solution:

   • Since the inequality includes \( \geq \), we will use a closed circle at \( 4 \) to indicate that \( 4 \) is included in the solution.
   • Draw a ray extending to the right from \( 4 \) to indicate all numbers greater than \( 4 \).

Graph:

• The graph should look like this:

<---●======================>
     4

• The closed circle (●) at 4 signifies that 4 is included in the solution, and the arrow indicates that the solution continues infinitely to the right.

Thus, the final solution is \( m \geq 4 \), and the graph reflects that the values of \( m \) that satisfy the inequality include \( 4 \) and all numbers greater than \( 4 \).