We are tasked with solving the inequality:

\[
1 - 10x + 25 > 0
\]

### Step 1: Combine like terms
Simplify the constants:

\[
26 - 10x > 0
\]

### Step 2: Isolate the variable
Subtract 26 from both sides:

\[
-10x > -26
\]

### Step 3: Solve for \( x \)
Divide both sides by \(-10\). **Remember**, when dividing by a negative number, the inequality sign flips:

\[
x < \frac{-26}{-10} \quad \Rightarrow \quad x < 2.6
\]

### Final solution:
\[
x < 2.6
\]

This is the solution for the inequality.

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Do you have any questions or want further details on the steps? Here are some related problems to try:

1. Solve \( 3 - 5x + 12 > 0 \).
2. Solve \( 4 - 7x + 18 > 0 \).
3. Solve \( -8x + 16 > 0 \).
4. Solve \( 12x - 4 + 9 > 0 \).
5. Solve \( -2x + 3 < 5 \).

**Tip:** Always remember to flip the inequality sign when dividing or multiplying both sides by a negative number.

Learn how to solve the linear inequality 1 - 10x + 25 > 0 step-by-step. This problem covers algebraic concepts and explains how to handle inequalities when dividing by a negative number. Suitable for students in Grades 8-10.

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