find the interval satisfying the inequality 4 - (1/2)n < -7 + (1/4)n,

To find the interval satisfying the inequality 4 - (1/2)n < -7 + (1/4)n, we can solve it step by step. Let's begin:

4 - (1/2)n < -7 + (1/4)n

First, let's eliminate the fractions by multiplying the entire inequality by the least common multiple (LCM) of the denominators, which is 4. This gives:

4 * (4 - (1/2)n) < 4 * (-7 + (1/4)n)

Simplifying:

16 - 2n < -28 + n

Now, let's isolate the variable n on one side of the inequality. We can do this by adding 2n to both sides and adding 28 to both sides:

16 - 2n + 2n < -28 + n + 2n + 28

16 < 3n

Finally, divide both sides of the inequality by 3:

16/3 < n

So, the solution to the inequality is n > 16/3.

Therefore, the interval satisfying the inequality is (16/3, ∞), where n is greater than 16/3.