https://file.aiquickdraw.com/mathbot/file/17288630008771rxomcyw.jpg

The image shows the following equation:

\[
\frac{x - 3}{2x + 4} = \frac{7}{6}
\]

Let's solve for \(x\).

### Step 1: Cross-multiply

To eliminate the fractions, we'll cross-multiply:

\[
6(x - 3) = 7(2x + 4)
\]

### Step 2: Expand both sides

Now, distribute the terms:

\[
6(x - 3) = 6x - 18
\]
\[
7(2x + 4) = 14x + 28
\]

So the equation becomes:

\[
6x - 18 = 14x + 28
\]

### Step 3: Move terms involving \(x\) to one side

To isolate \(x\), move all \(x\)-terms to one side of the equation and constants to the other side:

\[
6x - 14x = 28 + 18
\]

Simplifying:

\[
-8x = 46
\]

### Step 4: Solve for \(x\)

Now divide by \(-8\):

\[
x = \frac{46}{-8} = -\frac{23}{4}
\]

Thus, the solution is:

\[
x = -\frac{23}{4}
\]

Would you like any more details or further clarification on these steps?

Here are 5 questions to extend your understanding:
1. What happens if the denominator of a rational equation is zero?
2. How would you check if the solution \(x = -\frac{23}{4}\) satisfies the original equation?
3. What are the possible methods to solve rational equations like this one?
4. How can you simplify a complex rational expression?
5. What does cross-multiplying achieve in rational equations?

**Tip:** When solving rational equations, always check that your solution doesn't make any denominators zero, as that would be undefined.

Solve the equation (x - 3) / (2x + 4) = 7/6.

Learn how to solve the rational equation (x - 3) / (2x + 4) = 7/6 using cross-multiplication. This detailed solution includes expanding, simplifying, and solving for x, making it perfect for students in Grades 8-10.

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