To solve the equation:

$\frac{2x - 3}{x + 9} = \frac{3}{5}$

we can use cross-multiplication to eliminate the fractions. This gives:

$5(2x - 3) = 3(x + 9)$

Step 1: Distribute

Expand both sides:

$10x - 15 = 3x + 27$

Step 2: Move terms involving $x$ to one side

Subtract $3x$ from both sides:

$10x - 3x - 15 = 27$

which simplifies to:

$7x - 15 = 27$

Step 3: Move constants to the other side

Add $15$ to both sides:

$7x = 42$

Step 4: Solve for $x$

Divide by $7$:

$x = 6$

Solution

The solution is:

$x = 6$

Would you like more details or have any questions?

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1. What happens if the equation has variables on both sides?
2. How would this process change if the fractions had different denominators?
3. Can we solve this using substitution or elimination?
4. How can we verify the solution in the original equation?
5. What if the equation were an inequality?

Tip: Always check your solution by substituting it back into the original equation.