Solve 1/10x+1/39/10x+1/4frac{2}{3}(frac{9}{10}x)+216=x

$$\frac{ 1 }{ 10 } x+ \frac{ 1 }{ 3 } \frac{ 9 }{ 10 } x+ \frac{ 1 }{ 4 } \frac{ 2 }{ 3 } ( \frac{ 9 }{ 10 } x)+216 = x$$

Solve for x

$$x=480$$

Steps for Solving Linear Equation

Multiply \frac{1}{3} times \frac{9}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{10}x+\frac{1\times 9}{3\times 10}x+\frac{1}{4}\times \frac{2}{3}\times \frac{9}{10}x+216=x$$

Do the multiplications in the fraction \frac{1\times 9}{3\times 10}.

$$\frac{1}{10}x+\frac{9}{30}x+\frac{1}{4}\times \frac{2}{3}\times \frac{9}{10}x+216=x$$

Reduce the fraction \frac{9}{30} to lowest terms by extracting and canceling out 3.

$$\frac{1}{10}x+\frac{3}{10}x+\frac{1}{4}\times \frac{2}{3}\times \frac{9}{10}x+216=x$$

Combine \frac{1}{10}x and \frac{3}{10}x to get \frac{2}{5}x.

$$\frac{2}{5}x+\frac{1}{4}\times \frac{2}{3}\times \frac{9}{10}x+216=x$$

Multiply \frac{1}{4} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{5}x+\frac{1\times 2}{4\times 3}\times \frac{9}{10}x+216=x$$

Do the multiplications in the fraction \frac{1\times 2}{4\times 3}.

$$\frac{2}{5}x+\frac{2}{12}\times \frac{9}{10}x+216=x$$

Reduce the fraction \frac{2}{12} to lowest terms by extracting and canceling out 2.

$$\frac{2}{5}x+\frac{1}{6}\times \frac{9}{10}x+216=x$$

Multiply \frac{1}{6} times \frac{9}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{5}x+\frac{1\times 9}{6\times 10}x+216=x$$

Do the multiplications in the fraction \frac{1\times 9}{6\times 10}.

$$\frac{2}{5}x+\frac{9}{60}x+216=x$$

Reduce the fraction \frac{9}{60} to lowest terms by extracting and canceling out 3.

$$\frac{2}{5}x+\frac{3}{20}x+216=x$$

Combine \frac{2}{5}x and \frac{3}{20}x to get \frac{11}{20}x.

$$\frac{11}{20}x+216=x$$

Subtract x from both sides.

$$\frac{11}{20}x+216-x=0$$

Combine \frac{11}{20}x and -x to get -\frac{9}{20}x.

$$-\frac{9}{20}x+216=0$$

Subtract 216 from both sides. Anything subtracted from zero gives its negation.

$$-\frac{9}{20}x=-216$$

Multiply both sides by -\frac{20}{9}, the reciprocal of -\frac{9}{20}.

$$x=-216\left(-\frac{20}{9}\right)$$

Express -216\left(-\frac{20}{9}\right) as a single fraction.

$$x=\frac{-216\left(-20\right)}{9}$$

Multiply -216 and -20 to get 4320.

$$x=\frac{4320}{9}$$

Divide 4320 by 9 to get 480.

$$x=480$$