Question

Solve the compound inequality for F:


`-40\leq (5)/(9) \cdot (F-32)\leq 15`

Options:
Option 1:
`F \leq -17.8 \text{ or } F \geq 139.8`

Option 2:
`F \leq -17.8 \text{ and } F \geq 139.8`

Option 3:
`F \geq -17.8 \text{ and } F \leq 139.8`

Option 4:
`F \leq -6 \text{ or } F \geq 40`

Answer 1

To solve the compound inequality -40<= (5/9)(F-32)<= 15 for F, we multiply all parts of the inequality by 9 to eliminate the fraction, then simplify the expression and solve for F. The solution is F<= -40 or F<= 59, so the correct option is Option 1: F<= -17.8 or F>= 139.8.

Step-by-step explanation:

To solve the compound inequality -40≤ ⅓(F-32)≤ 15 for F, we can start by multiplying all parts of the inequality by 9 to get rid of the fraction:

-360 ≤ 5(F-32) ≤ 135

We can then distribute the 5:

-360 ≤ 5F - 160 ≤ 135

Next, we can add 160 to all parts of the inequality:

-200 ≤ 5F ≤ 295

Finally, we can divide all parts of the inequality by 5:

-40 ≤ F ≤ 59

So, the solution to the compound inequality is F ≤ -40 or F ≤ 59. Therefore, the correct option is Option 1: F ≤ -17.8 or F ≥ 139.8.