How Close Must x Be to 2 for 5x+3 to Be Within 0.075 of 13?

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Homework Help Overview

The problem involves determining how close the variable x must be to the value 2 so that the expression 5x + 3 remains within a distance of 0.075 from the number 13. This falls under the subject area of limits and inequalities in calculus.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the interpretation of the distance from 13 and how to set up the corresponding inequalities. There is an exploration of finding values of x that satisfy the condition for 5x + 3.

Discussion Status

The discussion is ongoing, with participants providing insights into the setup of the problem and exploring the implications of the inequalities. Some guidance has been offered regarding how to approach the solution, but there is no explicit consensus on the final steps or answers.

Contextual Notes

There is some confusion regarding the evaluation of the problem, and participants are questioning the clarity of the original question. Additionally, external resources have been suggested to aid understanding.

step1536
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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?
 
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 [itex]12.25\le 5x+ 3\le 13.75[/itex]. Solve that inequality for x. How close is that to 2?
 
I understand that part but how do you work the problem out?
 
so x=1.85,2.15; then I would then subtract 2-1.85 and 2-2.15. my answer would be .15
 
Hey step: check out this web site. i thought it was helpful (the "flash" examples in particular)

http://archives.math.utk.edu/visual.calculus/1/definition.6/index.html
 

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