Solve 4x/9+5x/24+20x/81+60/1=x

$$\frac { 4 x } { 9 } + \frac { 5 x } { 24 } + \frac { 20 x } { 81 } + \frac { 60 } { 1 } = x$$

Solve for x

$$x = \frac{7776}{13} = 598\frac{2}{13} \approx 598.153846154$$

Steps for Solving Linear Equation

Anything divided by one gives itself.

$$\frac{4x}{9}+\frac{5x}{24}+\frac{20x}{81}+60=x$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9 and 24 is 72. Multiply \frac{4x}{9} times \frac{8}{8}. Multiply \frac{5x}{24} times \frac{3}{3}.

$$\frac{8\times 4x}{72}+\frac{3\times 5x}{72}+\frac{20x}{81}+60=x$$

Since \frac{8\times 4x}{72} and \frac{3\times 5x}{72} have the same denominator, add them by adding their numerators.

$$\frac{8\times 4x+3\times 5x}{72}+\frac{20x}{81}+60=x$$

Do the multiplications in 8\times 4x+3\times 5x.

$$\frac{32x+15x}{72}+\frac{20x}{81}+60=x$$

Combine like terms in 32x+15x.

$$\frac{47x}{72}+\frac{20x}{81}+60=x$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 72 and 81 is 648. Multiply \frac{47x}{72} times \frac{9}{9}. Multiply \frac{20x}{81} times \frac{8}{8}.

$$\frac{9\times 47x}{648}+\frac{8\times 20x}{648}+60=x$$

Since \frac{9\times 47x}{648} and \frac{8\times 20x}{648} have the same denominator, add them by adding their numerators.

$$\frac{9\times 47x+8\times 20x}{648}+60=x$$

Do the multiplications in 9\times 47x+8\times 20x.

$$\frac{423x+160x}{648}+60=x$$

Combine like terms in 423x+160x.

$$\frac{583x}{648}+60=x$$

Subtract x from both sides.

$$\frac{583x}{648}+60-x=0$$

Subtract 60 from both sides. Anything subtracted from zero gives its negation.

$$\frac{583x}{648}-x=-60$$

Multiply both sides of the equation by 648.

$$583x-648x=-38880$$

Combine 583x and -648x to get -65x.

$$-65x=-38880$$

Divide both sides by -65.

$$x=\frac{-38880}{-65}$$

Reduce the fraction \frac{-38880}{-65} to lowest terms by extracting and canceling out -5.

$$x=\frac{7776}{13}$$