Question 1121431
|x-8.2| - 1.5 <= 0


add 1.5 to both sides to get |x-8.2| <= 1.5.


this means absolute value of (x - 8.2) is smaller than or equal to 1.5.


when (x - 8.2) is positive, the formula becomes (x - 8.2) <= 1.5.


add 8.2 to both sides to get x <= 8.2 + 1.5 which becomes x <= 9.7.


when (x - 8.2) is negative,the formula becomes (x - 8.2) >= -1.5.


add 8.2 to both sides gets x >= 6.7.


yor solution is x >= 6.7 and x <= 9.7.


this can be written as 6.7 <= x <= 9.7


that's your solution.


here's a reference that includes a calculator.


<a href = "https://www.mathpapa.com/absolute-value-equation-calculator/?q=3%7C2x%2B1%7C%2B4%3D25" target = "_blank">https://www.mathpapa.com/absolute-value-equation-calculator/?q=3%7C2x%2B1%7C%2B4%3D25</a>


here's a display of my use of this calculator to solve your problem.


<img src= "http://theo.x10hosting.com/2018/082201.jpg" alt="$$$" >


<img src= "http://theo.x10hosting.com/2018/082202.jpg" alt="$$$" >


<img src= "http://theo.x10hosting.com/2018/082203.jpg" alt="$$$" >


here's a reference on how to solve absolute value equations.


<a href = "https://www.varsitytutors.com/hotmath/hotmath_help/topics/absolute-value-inequalities" target = "_blank">https://www.varsitytutors.com/hotmath/hotmath_help/topics/absolute-value-inequalities</a>


there's lots of others on the web.


just do a search for "how to solve absolute value inequalities"