Lim (3-2x)=7 x->-2 I\'ve tried working it backwards: |3-2x-7|< E |-4-2x| < E 2 |

Question

Lim (3-2x)=7 x->-2   

I've tried working it backwards: |3-2x-7|< E |-4-2x| < E 2 | -2-x| < E |-2-x| < E/2 |x-c| < delta
I'm not sure if that right, but I'm thinking it's going to be DNE. Not sure how to write the proof. Lim (3-2x)=7 x->-2   

I've tried working it backwards: |3-2x-7|< E |-4-2x| < E 2 | -2-x| < E |-2-x| < E/2 |x-c| < delta
I'm not sure if that right, but I'm thinking it's going to be DNE. Not sure how to write the proof. Lim (3-2x)=7 x->-2   

I've tried working it backwards: |3-2x-7|< E |-4-2x| < E 2 | -2-x| < E |-2-x| < E/2 |x-c| < delta
I'm not sure if that right, but I'm thinking it's going to be DNE. Not sure how to write the proof.

Explanation / Answer

|3-2x-7|< E

==> |-4-2x| < E

==> 2 | -2-x| < E

==> |-2-x| < E/2

==> |-(2+x)| < E/2

==> |x+2| < E/2

==> |x-(-2)| < E/2

==> |x-c| < delta

where c = -2 , delta = E/2

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