Algebra-1

To solve for x given that the distance between point A (representing x) and point B (representing 5) is at most 12, we can set up the inequality based on the definition of distance.

The distance between two points on a number line is the absolute value of the difference between the numbers they represent.

So, the distance between point A (representing x) and point B (representing 5) is |x - 5|.

Then, we can set up the following inequality: |x - 5| ≤ 12.

For an inequality of the form |A| ≤ B, where A is an expression and B is a positive number, it can be rewritten as a compound inequality: -B ≤ A ≤ B. This inequality can be written as: -12 ≤ x - 5 ≤ 12.