Number Line Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
Find all integers within distance 2.52.5 of −1-1 on the number line.

Solution

  1. 1
    Distance ≤2.5\leq 2.5 means ∣x−(−1)∣≤2.5|x - (-1)| \leq 2.5, i.e., ∣x+1∣≤2.5|x + 1| \leq 2.5.
  2. 2
    Solve: −2.5≤x+1≤2.5-2.5 \leq x + 1 \leq 2.5, so −3.5≤x≤1.5-3.5 \leq x \leq 1.5.
  3. 3
    Integers in [−3.5,1.5][-3.5, 1.5]: −3,−2,−1,0,1-3, -2, -1, 0, 1.

Answer

The integers are −3,−2,−1,0,1-3, -2, -1, 0, 1.
Using the number line to solve distance inequalities translates an absolute value condition into an interval. The number line makes the solution visual: all numbers within a given radius of a centre point form a segment.

About Number Line

A straight line where each point represents a number, with equal spacing giving a visual model of all real numbers. The number line extends infinitely in both directions, with negative numbers to the left of zero and positive numbers to the right, providing a geometric representation of order and distance.

Learn more about Number Line →

More Number Line Examples

Example 1 easy

Plot and label the following on a number line: [formula], [formula], [formula], [formula], [formula]

Example 3 medium

On a number line, point A is at [formula] and point B is at [formula]. Find the midpoint and the dis

Example 4 easy

On a number line, point [formula] is at [formula] and point [formula] is at [formula]. Find the midp

Example 5 medium

A frog starts at [formula] on a number line. It jumps [formula], then [formula], then [formula], the

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