Question

1. one fourth of the opposite of the difference of five and a number is less than twenty.

Explanation:

Step1: Define the unknown number

Let the number be $x$.

Step2: Translate "difference of five and a number"

The difference is $5 - x$.

Step3: Find the opposite of the difference

Opposite: $-(5 - x) = x - 5$.

Step4: Take one fourth of this value

$\frac{1}{4}(x - 5)$

Step5: Set up the inequality

The result is less than 20:
$\frac{1}{4}(x - 5) < 20$

Step6: Solve the inequality

Multiply both sides by 4:
$x - 5 < 80$
Add 5 to both sides:
$x < 85$

Answer:

$x < 85$ (where $x$ is the unknown number)