N.5 Graph solutions to one-step inequalities

Question

TMX
Solve the inequality and graph the solution.
h
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 \( h/2 \geq 4 \), we will follow these steps:

1. Isolate \( h \):

   • Multiply both sides by 2 to eliminate the fraction: \[ h \geq 4 \times 2 \] \[ h \geq 8 \]

2. Graph the Solution:

   • The solution \( h \geq 8 \) means that \( h \) can be any number greater than or equal to 8.
   • The graph is represented on a number line:
     • Draw a closed dot (to indicate that 8 is included) on the number 8.
     • Draw a ray extending to the right to show all numbers greater than 8.

Here is a visual representation of the graph:

<----|----|----|----|----|----|----|----|----|----|---->
     6    7    8    9    10   11   12   13   14   15
          ●======================>

• The closed circle (●) at 8 indicates that 8 is included in the solution, while the arrow (➔) indicates that the solutions continue to the right indefinitely.