https://file.aiquickdraw.com/mathbot/file/1727658187285epvszbpl.jpg

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.

Solve the inequality |3 - 2x| < 5 and choose the correct answer from the options provided.

Learn how to solve the absolute value inequality |3 - 2x| < 5 with a detailed step-by-step solution. This problem explores key algebraic concepts including compound inequalities and the properties of absolute values. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation