SOLUTION: Dr. Jones has found that, over the years, 95% of the babies she has delivered weighed x pounds, where open vertical bar x minus 8.2 close vertical bar minus 1.5 space less or equal

Question 1121431: Dr. Jones has found that, over the years, 95% of the babies she has delivered weighed x pounds, where open vertical bar x minus 8.2 close vertical bar minus 1.5 space less or equal than space 0. Solve the inequality.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
|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.

https://www.mathpapa.com/absolute-value-equation-calculator/?q=3%7C2x%2B1%7C%2B4%3D25

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

$$$

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

https://www.varsitytutors.com/hotmath/hotmath_help/topics/absolute-value-inequalities

there's lots of others on the web.

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

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