Question

What is the length of the segment of the number line consisting of the points that satisfy (x-4)^2 less than or equal to 9?

Answer 1

After you take the square root, you find

... |x - 4| ≤ 3

... -3 ≤ x-4 ≤ 3

Since the coefficient of x is 1, the length of the solution space is the difference between +3 and -3, which is 6.

The length of the segment is 6.

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Going the rest of the way to a solution for x by adding 4 to the above inequality does not alter the difference between the high value and the low value.