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# 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.

Thank You!

### 1 Answer

- 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.

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