https://file.aiquickdraw.com/mathbot/file/17276677417833gp706ek.jpg

The equation you shared in the image is:

\[
\frac{3x - 9}{5} = \frac{7 - x}{3 - 9}
\]

Let's solve it step by step.

### Step 1: Simplify the denominator on the right-hand side
The denominator on the right-hand side is \(3 - 9 = -6\). So, the equation becomes:

\[
\frac{3x - 9}{5} = \frac{7 - x}{-6}
\]

### Step 2: Cross-multiply
We will cross-multiply to eliminate the fractions:

\[
(3x - 9)(-6) = (7 - x)(5)
\]

### Step 3: Expand both sides
Expand both sides of the equation:

\[
-6(3x - 9) = 5(7 - x)
\]

Left-hand side:
\[
-6(3x) + (-6)(-9) = -18x + 54
\]

Right-hand side:
\[
5(7) - 5(x) = 35 - 5x
\]

So, the equation is now:

\[
-18x + 54 = 35 - 5x
\]

### Step 4: Combine like terms
Move all the terms involving \(x\) to one side and the constant terms to the other side. Start by adding \(18x\) to both sides:

\[
54 = 35 + 13x
\]

Now, subtract \(35\) from both sides:

\[
54 - 35 = 13x
\]

\[
19 = 13x
\]

### Step 5: Solve for \(x\)
Divide both sides by 13:

\[
x = \frac{19}{13}
\]

So, the solution is:

\[
x = \frac{19}{13}
\]

Would you like any further details or have any questions about this solution?

Here are some related questions:
1. What happens if the equation involves more complex denominators?
2. How does cross-multiplying help solve equations with fractions?
3. Can you explain how to check if this solution satisfies the original equation?
4. What other methods could be used to solve rational equations?
5. How can simplifying the expression first make the equation easier to solve?

**Tip:** When solving equations with fractions, cross-multiplying is a very effective method, but always check for any restrictions in the denominators to avoid dividing by zero!

Solve the equation: (3x - 9) / 5 = (7 - x) / (3 - 9)

Learn how to solve the rational equation (3x - 9)/5 = (7 - x)/-6 using cross-multiplication. This problem covers important algebraic concepts related to solving equations with fractions. Suitable for students in Grades 8-10.

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