Solve (350 + 6X)/16 = (450 - 6X)/9 for X.

Step-by-step solution

1. 1

   Recognise the equation as a proportion. Each side is a single fraction, so cross-multiplication applies directly. Both denominators are nonzero constants, so there is no domain restriction to worry about here.

2. 2

   Cross-multiply. Multiply each numerator by the opposite denominator:

   $9(350+6X)=16(450-6X)$

3. 3

   Expand both sides. Keep the sign on the $-6X$ term when distributing $16$:

   $3150+54X=7200-96X$

4. 4

   Gather the $X$ terms on one side and the constants on the other. Add $96X$, then subtract $3150$:

   $3150+150X=7200\quad\Longrightarrow\quad 150X=4050$

5. 5

   Divide to finish.

   $X=\frac{4050}{150}=27$

6. 6

   Substitute back into the original fractions. With $X=27$: the left side is $\dfrac{350+162}{16}=\dfrac{512}{16}=32$, and the right side is $\dfrac{450-162}{9}=\dfrac{288}{9}=32$. Both equal $32$, so $X=27$ is confirmed.