Question

the inequality |t-57|<7 describes the range of monthly average temperature, T, in Degrees Fahrenheit, for san Francisco, California. solve the inequality and interperet the solution

Answer 1

Solution is:  $50\leq T\leq 64$ and it means, the minimum temperature is 50° Fahrenheit and the maximum temperature is 64° Fahrenheit.

Explanation

Given inequality is:   $|T-57|\leq 7$

As this is absolute inequality, so we will get two different inequalities-- one for positive and another for negative. So.....

$T-57\leq 7\\ \\ T\leq 7+57\\ \\ T\leq 64$

and

$-(T-57)\leq 7\\ \\ -T+57\leq 7\\ \\ -T\leq 7-57\\ \\ -T\leq -50\\ \\ T\geq 50$

So, the final combined solution will be:  $50\leq T\leq 64$

It means that the minimum temperature for San Francisco, California is 50° Fahrenheit and the maximum temperature is 64° Fahrenheit.