Clearly for -19 <= x <= 22 the sum is constant at 41.
On each end of the interval, the sum rises by 2 for each change of 1 in x.
Since 137-41 = 96, divide that by 2 to see that as long as x is within 48 of the endpoints of [-19,22] the sum is within 96 of 41.
So, -67 <= x <= 70
Let a and b be the maximum and minimum value of x, respectively, satisfying the inequality |x+19|+|x−22|≤137, then what is a−b?
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