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Let's solve the inequality step by step:

The inequality given is:
\[
-x + 25 < \frac{1}{2}x + 1
\]

### Step 1: Eliminate the fraction.
To make the equation easier to handle, first eliminate the fraction by multiplying every term by 2.

\[
2(-x + 25) < 2\left(\frac{1}{2}x + 1\right)
\]

This simplifies to:
\[
-2x + 50 < x + 2
\]

### Step 2: Bring all terms involving \(x\) to one side.
Move all \(x\)-terms to the left side and constant terms to the right side:

\[
-2x - x < 2 - 50
\]

This simplifies to:
\[
-3x < -48
\]

### Step 3: Solve for \(x\).
Now, divide both sides by \(-3\), but remember that dividing or multiplying an inequality by a negative number reverses the inequality sign:

\[
x > 16
\]

### Step 4: Express the solution in interval notation.
The solution \(x > 16\) means that \(x\) is greater than 16. In interval notation, this is:

\[
(16, \infty)
\]

### Final Answer:
The solution in interval notation is \( \boxed{(16, \infty)} \).

Do you have any questions or need further clarification?

Here are some related questions you might find useful:
1. What happens if I multiply both sides of an inequality by a negative number?
2. How can I solve inequalities with multiple fractions?
3. What is the difference between solving inequalities and equations?
4. How do you graph an inequality solution on a number line?
5. Can inequalities have more than one solution?

**Tip:** When solving inequalities, always remember to reverse the inequality sign when multiplying or dividing by a negative number.

Solve the inequality and write the answer using interval notation: -x + 25 < (1/2)x + 1.

Learn how to solve the inequality -x + 25 < (1/2)x + 1 with detailed steps and explanations. This problem focuses on solving inequalities and involves algebraic manipulation. Suitable for students in Grades 8-10.

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