N.5 Graph solutions to one-step inequalities

Question

TMX
Solve the inequality and graph the solution.
a–5>3
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 \( a - 5 > 3 \), follow these steps:

1. Isolate the variable: \[ a - 5 > 3 \] Add 5 to both sides: \[ a > 3 + 5 \] Simplifying gives: \[ a > 8 \]

2. Graph the solution:

   • On a number line, place an open circle at 8 (since the inequality is \( a > 8 \) and does not include 8).
   • Draw a ray starting from 8 and extending to the right, indicating that all numbers greater than 8 are included in the solution.

Visualization:

<---o===================>
     7  8  9  10  

Here, "o" at 8 represents an open circle, indicating that 8 is not included. The ray extending to the right shows that all numbers greater than 8 are part of the solution.