https://file.aiquickdraw.com/mathbot/file/1728403212221h9jw4xdy.jpg

We are tasked with solving the inequality:

\[
\frac{1 - x}{4} < \frac{2x - 2}{13}
\]

### Step-by-step solution:

1. **Eliminate the denominators** by multiplying both sides of the inequality by the least common denominator (LCD) of 4 and 13, which is 52. This removes the fractions:

\[
52 \times \frac{1 - x}{4} < 52 \times \frac{2x - 2}{13}
\]

This simplifies to:

\[
13(1 - x) < 4(2x - 2)
\]

2. **Distribute** on both sides:

\[
13 - 13x < 8x - 8
\]

3. **Combine like terms** by first isolating all the terms with \(x\) on one side and constants on the other:

\[
13 + 8 < 8x + 13x
\]

This simplifies to:

\[
21 < 21x
\]

4. **Solve for \(x\)** by dividing both sides by 21:

\[
x > 1
\]

### Final Answer:
In interval notation, the solution is:

\[
(1, \infty)
\]

Would you like any further details or have any questions? Here are some related questions for further practice:

1. How do you solve inequalities with fractions?
2. What is the least common denominator, and why is it used?
3. How does solving inequalities differ from solving equations?
4. How do you express inequalities in interval notation?
5. What happens when you multiply or divide an inequality by a negative number?

**Tip:** Always remember to reverse the inequality sign if you multiply or divide both sides by a negative number!

Solve the inequality symbolically: (1 - x)/4 < (2x - 2)/13. Express the solution set in interval notation.

Learn how to solve the inequality (1 - x)/4 < (2x - 2)/13 and express the solution in interval notation. This step-by-step solution involves cross-multiplication and the properties of inequalities. Suitable for students in Grades 8-10.

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