To solve the absolute value inequality 2|x| < 5, we first isolate the absolute value.
1. Divide both sides by 2:
|x| < 2.5
2. Now we can rewrite the absolute value inequality as two separate inequalities:
-2.5 < x < 2.5
This means that x can take any value between -2.5 and 2.5, not including -2.5 and 2.5 themselves.
3. To graph this solution on a number line, we can draw a line starting from -2.5 to 2.5, and use open circles at both ends to indicate that these endpoints are not included in the solution. Shade the region between -2.5 and 2.5.
In conclusion, the solution to the inequality is:
-2.5 < x < 2.5
And the graph would look like a line segment between -2.5 and 2.5 with open circles at both ends.