Integer Solutions |x| < N

Free interactive math game: Integer Solutions |x| < N — How many integers?. Part of the Absolute Value category on MathKite.

Example problems

Taken from the generator that powers this exercise. A fresh set appears every time the page is opened, and the printable worksheet holds ten of them.

  1. |x| < 6 — How many integer solutions?
  2. |x| ≤ 6 — How many integer solutions?
  3. |x| < 4 — How many integer solutions?
  4. |x| ≤ 3 — How many integer solutions?

About this exercise

Counting the whole numbers that satisfy an absolute-value inequality.

How to solve it

Find the interval the inequality describes, then count the integers inside it, watching whether the endpoints belong.

Worked example

Absolute value of x at most 3 holds for -3, -2, -1, 0, 1, 2 and 3 — seven integers.

Common mistake

Forgetting zero. It sits in nearly every such interval and is easily skipped.