−20 ≤ 59(F−32) ≤ −15

We take the value of F in the inequality by taking the inequalities in group. Let the first group be:

(1)    -20 ≤ 59(F - 32)

Then, the second group would be,
(2)     59(F - 32) ≤ - 15

Calculating for the values of F,

(1)     -20 ≤ 59F - 1888
          1888 - 20 ≤ 59F
              1868 ≤ 59F
                 F ≥ 31.66

(2)     (59)(F - 32) ≤ - 15
             59F - 1888 ≤ -15
             59F ≤ 1873
                F ≤ 31.75

The values of F are therefore,
               31.66 ≤ F ≤ 31.75