Distance on a number line

If a and b are two points on a number line then the distance from a to b is |a-b|.

Exercises

1.

How far is it from -1 -7? Illustrate your answer.

2.

What is the set of all number that are within 5 of -2? Illustrate your answer.

3.

Interpret the inequality |x - 4| < 1/20 geometrically. Illustrate your answer, and solve the inequality |x - 4| < 1/20.

4.

Solve the inequality |x + 4| < 1/10 geometrically. Hint: x+4 = x -(-4).