Algebra

We are given two inequalities: We will solve each inequality and then find the common solution. Step 1: Solve the first inequality.
From the inequality , we add 1 to both sides: Now, divide both sides by 2:
Step 2: Solve the second inequality.
From the inequality , we add 9 to both sides: Now, divide both sides by 2:
Step 3: Combine the two results.
We now have: Thus, the solution is .
Step 4: Conclusion.
The correct option is (C) .

Step 1: Solve the given equation .

We start with the equation:

We can rewrite 27 and 9 as powers of 3:

Thus, the equation becomes:

Combine the exponents:

Since the bases are the same, equate the exponents:

Rearranging terms:

Factoring:

So the possible values of are: or

Step 2: Evaluate

For :

For :


Therefore, the value is , which corresponds to Option (C).