So you could take e.g. delta = (0.1)/5 = 0.02 in the first question and delta = (0.01)/5 = 0.002 in the second. These are the largest possible values of delta that will work for these problems. It is worth pointing out that if one delta will do as an answer in a question of this type, so will any positive number smaller than that delta. For example in the first problem, if |x - 1| < 0.0000002343890382324, then certainly also |x - 1| < 0.02 holds, so from the analysis we did for this larger number we know that |5x - 5| < 0.01. Questions of this type never have only one answer.
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If |x - 1| < e/5 then
|5x - 5| = |5(x - 1)| = 5 |x - 1| < 5 (e/5)
so in particular |5x - 5| < e.
So you could take e.g. delta = (0.1)/5 = 0.02 in the first question and delta = (0.01)/5 = 0.002 in the second. These are the largest possible values of delta that will work for these problems. It is worth pointing out that if one delta will do as an answer in a question of this type, so will any positive number smaller than that delta. For example in the first problem, if |x - 1| < 0.0000002343890382324, then certainly also |x - 1| < 0.02 holds, so from the analysis we did for this larger number we know that |5x - 5| < 0.01. Questions of this type never have only one answer.