How do you find the absolute value equation of a number line?
I can't figure out how to determine the absolute value equation of two problems.
Show work please. I need to know how to solve this by tomorrow.
1. x≤4 and x≥10 (Indicated on the number line.)
2. -5≤x≤3 (Indicated on the number line.)
Please help me quickly. I have a test soon.
- norcekriLv 77 years agoFavorite Answer
These things hinge on difference from the range's midpoint. The general form is
| x - midpoint | < half-range
This is for an inclusive range, such as your second problem. For an exclusive range, such as the first one, flip the sign.
I'll work through one ...
midpoint = (4 + 10) / 2 = 14/2 = 7
half-range = (10 - 4) / 2 = 6/2 = 3
| x-7 | >= 3 (note that we have to include = when the desired solution includes =. )
See how that works?
The second one has a midpoint of -1 and a half-range of 4.