Answer
The absolute value inequality is
| x - 24 | > 6.5
So, the solution of the absolute value inequality is
x < 17.5 inches
OR
x > 30.5 inches
Step-by-step explanation
The mean amount of rainfall is 24 inches.
In 90% of the last 30 years, the rainfall at Shell Beach varied no more than 6.5 inches from the mean.
We are told to write and solve an absolute value inequality to describe the rainfall in the other 10% of the last 30 years.
In the remaining 10% of the last 30 years, the anount of rainfall at the Shell Beach will vary more than 6.5 inches from the mean of 24 inches.
Let the amount of rainfall in the remaining 10% of the last 30 years be x.
The absolute value inequality will thus be
| x - 24 | > 6.5
To solve an expression with the absolute value symbol. we obtain two solutions for it.
We first solve when the other side of the equation to the absolute value symbol has positive sign.
Then, we obtain another solution by setting that other side (the right hand side) to negative. For equations involving inequality signs, the second solution usually changes the inequality sign.
| x - 24 | > 6.5
(x - 24) > 6.5
x > 6.5 + 24
x > 30.5 inches
OR
(x - 24) < -6.5
x < -6.5 + 24
x < 17.5 inches.
So, the solution of the absolute value inequality is
x < 17.5 inches
OR
x > 30.5 inches
Hope this Helps!!!