Question

What’s a more efficient way to describe ""the set of all numbers at most 4 units away from 2""

Answer 1

the solution is a set of real numbers between the intervals of -2 and 6

Explanation:

We want to represent the set of all numbers at most 4 units away from 2.

If the numbers are represented by "x", this means that we want the distance between x and 2 to be less than or equal to 4.

Now, the distance between x and 2 can be represented in absolute value form as; |x - 2|

Thus, the equation that satisfies the more efficient way is;

|x - 2| ≤ 4

This means that;

x - 2 ≤ 4 or x - 2 ≥ -4

Solving both we have;

x ≤ 6 or x ≥ -2

Thus, the solution is a set of real numbers between the intervals of -2 and 6