# Precise Definition of a limit

## The Attempt at a Solution

How close to 2 do we have to take x so that 5x+3 is within a distance of 0.075 from 13.
I am confuse on how to evaluate this problem.

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You should state your question more clearly.

A distance of 0.075 from 13 can be 13 + 0.075 or 13 - 0.075. Can you find an x such that 5x+3 evaluates to one of those two points?

HallsofIvy
5x+3 will be within distance 0.075 from 13 (above or below) as long as 5x+ 3 is between 13- 0.75 and 13+ 0.75 or $12.25\le 5x+ 3\le 13.75$. Solve that inequality for x. How close is that to 2?