Graph the solution to the inequality on the number line
|4u-8|=>12
u <= -1 or u >= 5
draw a dot at -1 and shade to the left
draw a dot at 5 and shade to the right
you can see the graph at
http://www.wolframalpha.com/input/?i=solve+|4u-8|+%3E%3D+12+
To graph the solution to the inequality |4u-8| >= 12 on the number line, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.
Case 1: 4u - 8 >= 12
Solving this inequality:
4u >= 20
u >= 5
In this case, u is greater than or equal to 5.
Case 2: -(4u - 8) >= 12
Solving this inequality:
-4u + 8 >= 12
-4u >= 4
u <= -1
In this case, u is less than or equal to -1.
Taking both cases into account, the solution to the inequality is u <= -1 or u >= 5. This means that u can take any value less than or equal to -1 or any value greater than or equal to 5.
To graph this on the number line, you can:
1. Draw a number line with 0 at the center.
2. Mark a solid dot at -1 to represent u <= -1.
3. Mark another solid dot at 5 to represent u >= 5.
4. Shade the region to the left of -1 and the region to the right of 5 to show that u can take any value in those regions.
The resulting graph will have a solid dot at -1, a solid dot at 5, and shaded regions to the left of -1 and to the right of 5.