Find a number δ such that if | x - 3 | < δ, then | 2x - 6 | < ε, where ε = 1?

Question

δ- is distance

Answer 1

1/2

|2x-6|=2|x-3|

so when |x-3|&lt;1/2, 2|x-3|&lt;1, and so |2x-6|&lt;1

Answer 2

e = 1 =&gt;

     |2x - 6| &lt; 1

        =&gt;  2|x - 3| &lt; 1

  

        =&gt;    |x -3| &lt; 0.5

         =&gt; d = 0.5