https://file.aiquickdraw.com/mathbot/file/1726486316641iv4sprea.jpg

The image shows the following mathematical expression:

\[
0 = \frac{8 - 2x}{1 - 2x}
\]

To solve for \( x \), let's proceed step by step.

### Step 1: Simplify the equation

\[
0 = \frac{8 - 2x}{1 - 2x}
\]

For this fraction to equal zero, the numerator must be zero. Therefore, we set the numerator equal to zero:

\[
8 - 2x = 0
\]

### Step 2: Solve for \( x \)

\[
8 = 2x
\]
\[
x = \frac{8}{2}
\]
\[
x = 4
\]

### Step 3: Check for restrictions

However, we must also check if \( x = 4 \) causes the denominator to become zero. The denominator is \( 1 - 2x \). If we plug \( x = 4 \) into the denominator:

\[
1 - 2(4) = 1 - 8 = -7
\]

Since the denominator does not become zero, \( x = 4 \) is a valid solution.

### Final Solution:
\[
x = 4
\]

Would you like more details or explanations on any of the steps?

---

Here are 5 related questions:
1. How do we handle cases where the denominator becomes zero?
2. What happens if both the numerator and denominator equal zero?
3. How do you solve equations with multiple variables?
4. How can this type of equation arise in real-world applications?
5. What is the effect of simplifying both sides of an equation before solving?

**Tip:** Always check the denominator for values of \(x\) that make it zero, as those are excluded from the solution set.

Solve the equation: 0 = (8 - 2x) / (1 - 2x)

This page provides a step-by-step guide on solving the rational equation 0 = (8 - 2x) / (1 - 2x). Learn how to simplify rational expressions and solve for x. 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