Let's solve the equation \( 1 = \frac{7 - 2x}{2 + 7x} \).

### Step 1: Cross-multiply to eliminate the fraction
To eliminate the fraction, we multiply both sides of the equation by \( 2 + 7x \):

\[
1 \times (2 + 7x) = 7 - 2x
\]

So, we get:

\[
2 + 7x = 7 - 2x
\]

### Step 2: Rearrange the equation to collect like terms
Next, we'll move all the \( x \) terms to one side and the constant terms to the other:

\[
7x + 2x = 7 - 2
\]

Simplifying, we get:

\[
9x = 5
\]

### Step 3: Solve for \( x \)
Now, divide both sides by 9:

\[
x = \frac{5}{9}
\]

So, the solution is:

\[
\boxed{x = \frac{5}{9}}
\]

Would you like more details or have any questions?

### Related Questions
1. How would you solve \( \frac{3x - 4}{2x + 5} = 2 \)?
2. What happens if the equation was \( 1 = \frac{7 - 2x}{2 - 7x} \) instead?
3. Can you find the solution to \( 2x + 3 = \frac{4x + 7}{5} \)?
4. What are the implications of having a negative denominator in the original equation?
5. How do you solve a system of equations that includes a similar rational equation?

### Tip
When solving equations involving fractions, always check if the denominator could potentially make the fraction undefined by setting the denominator equal to zero and ensuring your solution does not make this true.

Learn how to solve the equation (7-2x)/(2+7x) = 1 step-by-step with a detailed solution. This problem involves rational expressions and cross-multiplication methods. Suitable for advanced high school students and beyond.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation