https://file.aiquickdraw.com/mathbot/file/1725594263978ivq05reu.jpg

The equation displayed in the image is:

\[
\frac{7}{9}x = \frac{8}{7}x + \frac{1}{63}
\]

Let's solve this step-by-step.

### Step 1: Eliminate the fractions.
To eliminate the fractions, multiply the entire equation by the least common denominator (LCD) of all the denominators involved. The denominators are \(9\), \(7\), and \(63\), and the LCD is \(63\).

Multiply the entire equation by \(63\):

\[
63 \cdot \frac{7}{9}x = 63 \cdot \frac{8}{7}x + 63 \cdot \frac{1}{63}
\]

Simplify:

\[
7 \cdot 7x = 9 \cdot 8x + 1
\]

This gives us:

\[
49x = 72x + 1
\]

### Step 2: Move all terms involving \(x\) to one side.
Subtract \(72x\) from both sides:

\[
49x - 72x = 1
\]

This simplifies to:

\[
-23x = 1
\]

### Step 3: Solve for \(x\).
Divide both sides by \(-23\):

\[
x = -\frac{1}{23}
\]

Thus, the solution is:

\[
x = -\frac{1}{23}
\]

Would you like a detailed explanation of any step, or do you have any questions?

Here are 5 related questions you might consider:
1. What are some techniques for solving equations with fractions?
2. How do you find the least common denominator of multiple fractions?
3. How can you check if the solution to a linear equation is correct?
4. What are the differences between linear and nonlinear equations?
5. How can we handle equations where the variable appears on both sides?

**Tip:** When dealing with fractions in equations, clearing them by multiplying through by the least common denominator simplifies the problem significantly!

Solve for x in the equation: (7/9)x = (8/7)x + 1/63

Discover how to solve linear equations with fractions using LCD multiplication and variable isolation. This guide provides a detailed walkthrough of solving the equation (7/9)x = (8/7)x + 1/63, suitable for high school students in grades 9-12.

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