N.5 Graph solutions to one-step inequalities

Question

TMX
Solve the inequality and graph the solution.
a
3
<2
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 \( 3 < 2 \), we first realize that the statement itself is not correct – \( 3 \) is not less than \( 2 \). However, if there is a misunderstanding and you meant a different inequality, such as \( x + 3 < 2 \), we can go through that example instead.

Example: Solve the Inequality \( x + 3 < 2 \)

1. Isolate \( x \): \[ x + 3 < 2 \] Subtract \( 3 \) from both sides: \[ x < 2 - 3 \] \[ x < -1 \]

2. Graph the Solution:

   • The solution to \( x < -1 \) means that \( x \) can be any number less than \(-1\).
   • To graph this inequality:
     • Plot the point at \(-1\).
     • Since this is a strict inequality (less than, not less than or equal to), we draw an open circle at \(-1\).
     • Draw a ray extending to the left (towards negative infinity) from the open circle at \(-1\).

Graphic Representation:

• On a number line:
  • Place an open circle on \(-1\).
  • Draw an arrow to the left from that point.

This indicates that all values left of \(-1\) are included in the solution set while \(-1\) itself is not included.

If you were asking about a different inequality, please let me know!