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

Step-by-step solution

1. 1

   Simplify inside the numerators first. The right numerator has two like terms:

   $450X-6X=444X$

   so the equation is

   $\frac{350+6X}{16}=\frac{444X}{9}$

2. 2

   Cross-multiply. Both denominators are nonzero constants, so multiply both sides by $16\cdot 9=144$:

   $9\left(350+6X\right)=16\left(444X\right)$

3. 3

   Expand both sides.

   $3150+54X=7104X$

4. 4

   Collect the $X$-terms on one side. Subtracting $54X$:

   $3150=7050X$

5. 5

   Reduce the fraction to lowest terms — carefully. $X=\dfrac{3150}{7050}$. Factoring, $3150=2\cdot 3^{2}\cdot 5^{2}\cdot 7$ and $7050=2\cdot 3\cdot 5^{2}\cdot 47$, so $\gcd=2\cdot 3\cdot 5^{2}=150$ and

   $X=\frac{3150\div 150}{7050\div 150}=\frac{21}{47}\approx 0.4468$

6. 6

   Check both sides independently. With $X=\dfrac{21}{47}$: the left side is $\dfrac{350+126/47}{16}=\dfrac{16576/47}{16}=\dfrac{1036}{47}$, and the right side is $\dfrac{444\cdot 21/47}{9}=\dfrac{9324/47}{9}=\dfrac{1036}{47}$. They match, so $X=\dfrac{21}{47}$ is correct — note that a common wrong reduction of $\dfrac{3150}{7050}$ to $\dfrac{7}{157}$ fails this check outright ($21.89$ versus $2.20$).