Solve 9(4-9/14x)/5(4+frac{5{14}x)}=5/9

$$\frac{ 9(4- \frac{ 9 }{ 14 } x) }{ 5(4+ \frac{ 5 }{ 14 } x) } = \frac{ 5 }{ 9 }$$

Solve for x

$$x = \frac{224}{61} = 3\frac{41}{61} \approx 3.672131148$$

Steps for Solving Linear Equation

Factor the expressions that are not already factored in \frac{9\left(4-\frac{9}{14}x\right)}{5\left(4+\frac{5}{14}x\right)}.

$$\frac{\frac{1}{14}\times 9\left(-9x+56\right)}{\frac{1}{14}\times 5\left(5x+56\right)}=\frac{5}{9}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{9\left(-9x+56\right)}{5\times \left(\frac{1}{14}\right)^{0}\left(5x+56\right)}=\frac{5}{9}$$

Calculate \frac{1}{14} to the power of 0 and get 1.

$$\frac{9\left(-9x+56\right)}{5\times 1\left(5x+56\right)}=\frac{5}{9}$$

Multiply 5 and 1 to get 5.

$$\frac{9\left(-9x+56\right)}{5\left(5x+56\right)}=\frac{5}{9}$$

Use the distributive property to multiply 9 by -9x+56.

$$\frac{-81x+504}{5\left(5x+56\right)}=\frac{5}{9}$$

Use the distributive property to multiply 5 by 5x+56.

$$\frac{-81x+504}{25x+280}=\frac{5}{9}$$

Variable x cannot be equal to -\frac{56}{5} since division by zero is not defined. Multiply both sides of the equation by 45\left(5x+56\right), the least common multiple of 25x+280,9.

$$9\left(-81x+504\right)=25\left(5x+56\right)$$

Use the distributive property to multiply 9 by -81x+504.

$$-729x+4536=25\left(5x+56\right)$$

Use the distributive property to multiply 25 by 5x+56.

$$-729x+4536=125x+1400$$

Subtract 125x from both sides.

$$-729x+4536-125x=1400$$

Combine -729x and -125x to get -854x.

$$-854x+4536=1400$$

Subtract 4536 from both sides.

$$-854x=1400-4536$$

Subtract 4536 from 1400 to get -3136.

$$-854x=-3136$$

Divide both sides by -854.

$$x=\frac{-3136}{-854}$$

Reduce the fraction \frac{-3136}{-854} to lowest terms by extracting and canceling out -14.

$$x=\frac{224}{61}$$