Let x represent temperature of the ocean.
We have been given that the temperature of the ocean at Huntington Beach can vary up to 8.6°F from the average temperature of 75°F. We are asked to write an absolute value equation to find the temperature extremes of the ocean.
We will use tolerance formula to solve our given problems.
[tex]|\text{Actual}-\text{Ideal}|\leq\text{Tolerance}[/tex]
Upon substituting our given values in above formula, we will get:
[tex]|x-75|\leq 8.6[/tex]
Therefore, our required inequality would be [tex]|x-75|\leq 8.6[/tex].
Using absolute value rule [tex]\text{If }|u|\leq a,\text{ then } -a\leq u\leq a[/tex], we will get:
[tex]-8.6\leq x-75\leq 8.6[/tex]
[tex]-8.6+75\leq x-75+75\leq 8.6+75[/tex]
[tex]66.4\leq x\leq 83.6[/tex]
Therefore, the temperature extremes of the ocean would be [tex]66.4\leq x\leq 83.6[/tex].
