The problem you provided asks to solve the inequality $|3 - 2x| < 5$ and choose the correct answer from the given options.

Let's solve the inequality step by step:

1. Start with the absolute value inequality: $|3 - 2x| < 5$

2. Rewrite as a compound inequality (because of the absolute value): $-5 < 3 - 2x < 5$

3. Solve the compound inequality:

   • First, subtract 3 from all parts of the inequality: $-5 - 3 < -2x < 5 - 3$ $-8 < -2x < 2$
   • Next, divide by $-2$ and reverse the inequality signs (since we are dividing by a negative number): $\frac{-8}{-2} > x > \frac{2}{-2}$ $4 > x > -1$
   • This simplifies to: $-1 < x < 4$

The solution is that $x$ is between $-1$ and $4$, which corresponds to option C: $-1 < x < 4$.

Would you like more details on the solution, or do you have any specific questions? Here are 5 related questions to explore further:

1. How do you solve absolute value inequalities in general?
2. Why do we reverse the inequality sign when dividing by a negative number?
3. How would the solution change if the inequality were $|3 - 2x| > 5$?
4. What is the difference between "and" and "or" solutions in compound inequalities?
5. How do we graph the solution $-1 < x < 4$ on a number line?

Tip: When solving inequalities with absolute values, always break them into two cases (positive and negative) before solving.