Solve =[23/90:(1/5-1/15)+10/3*frac{3}{10}-frac{1}{4}]=(frac{2}{9}-frac{1}{54}*3+frac{4}{3}):x

$$= [ \frac { 23 } { 90 } : ( \frac { 1 } { 5 } - \frac { 1 } { 15 } ) + \frac { 10 } { 3 } \cdot \frac { 3 } { 10 } - \frac { 1 } { 4 } ] = ( \frac { 2 } { 9 } - \frac { 1 } { 54 } \cdot 3 + \frac { 4 } { 3 } ) : x$$

Solve for x

$$x=\frac{9}{16}=0.5625$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 60x, the least common multiple of 3,10,4,x.

$$450x\times \frac{23}{90}+\frac{10}{3}\times \frac{3}{10}\times 60x+60x\left(-\frac{1}{4}\right)=60\left(\frac{2}{9}-\frac{1}{54}\times 3+\frac{4}{3}\right)$$

Express 450\times \frac{23}{90} as a single fraction.

$$\frac{450\times 23}{90}x+\frac{10}{3}\times \frac{3}{10}\times 60x+60x\left(-\frac{1}{4}\right)=60\left(\frac{2}{9}-\frac{1}{54}\times 3+\frac{4}{3}\right)$$

Multiply 450 and 23 to get 10350.

$$\frac{10350}{90}x+\frac{10}{3}\times \frac{3}{10}\times 60x+60x\left(-\frac{1}{4}\right)=60\left(\frac{2}{9}-\frac{1}{54}\times 3+\frac{4}{3}\right)$$

Divide 10350 by 90 to get 115.

$$115x+\frac{10}{3}\times \frac{3}{10}\times 60x+60x\left(-\frac{1}{4}\right)=60\left(\frac{2}{9}-\frac{1}{54}\times 3+\frac{4}{3}\right)$$

Cancel out \frac{10}{3} and its reciprocal \frac{3}{10}.

$$115x+60x+60x\left(-\frac{1}{4}\right)=60\left(\frac{2}{9}-\frac{1}{54}\times 3+\frac{4}{3}\right)$$

Combine 115x and 60x to get 175x.

$$175x+60x\left(-\frac{1}{4}\right)=60\left(\frac{2}{9}-\frac{1}{54}\times 3+\frac{4}{3}\right)$$

Express 60\left(-\frac{1}{4}\right) as a single fraction.

$$175x+\frac{60\left(-1\right)}{4}x=60\left(\frac{2}{9}-\frac{1}{54}\times 3+\frac{4}{3}\right)$$

Multiply 60 and -1 to get -60.

$$175x+\frac{-60}{4}x=60\left(\frac{2}{9}-\frac{1}{54}\times 3+\frac{4}{3}\right)$$

Divide -60 by 4 to get -15.

$$175x-15x=60\left(\frac{2}{9}-\frac{1}{54}\times 3+\frac{4}{3}\right)$$

Combine 175x and -15x to get 160x.

$$160x=60\left(\frac{2}{9}-\frac{1}{54}\times 3+\frac{4}{3}\right)$$

Multiply \frac{1}{54} and 3 to get \frac{3}{54}.

$$160x=60\left(\frac{2}{9}-\frac{3}{54}+\frac{4}{3}\right)$$

Reduce the fraction \frac{3}{54} to lowest terms by extracting and canceling out 3.

$$160x=60\left(\frac{2}{9}-\frac{1}{18}+\frac{4}{3}\right)$$

Least common multiple of 9 and 18 is 18. Convert \frac{2}{9} and \frac{1}{18} to fractions with denominator 18.

$$160x=60\left(\frac{4}{18}-\frac{1}{18}+\frac{4}{3}\right)$$

Since \frac{4}{18} and \frac{1}{18} have the same denominator, subtract them by subtracting their numerators.

$$160x=60\left(\frac{4-1}{18}+\frac{4}{3}\right)$$

Subtract 1 from 4 to get 3.

$$160x=60\left(\frac{3}{18}+\frac{4}{3}\right)$$

Reduce the fraction \frac{3}{18} to lowest terms by extracting and canceling out 3.

$$160x=60\left(\frac{1}{6}+\frac{4}{3}\right)$$

Least common multiple of 6 and 3 is 6. Convert \frac{1}{6} and \frac{4}{3} to fractions with denominator 6.

$$160x=60\left(\frac{1}{6}+\frac{8}{6}\right)$$

Since \frac{1}{6} and \frac{8}{6} have the same denominator, add them by adding their numerators.

$$160x=60\times \frac{1+8}{6}$$

Add 1 and 8 to get 9.

$$160x=60\times \frac{9}{6}$$

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

$$160x=60\times \frac{3}{2}$$

Express 60\times \frac{3}{2} as a single fraction.

$$160x=\frac{60\times 3}{2}$$

Multiply 60 and 3 to get 180.

$$160x=\frac{180}{2}$$

Divide 180 by 2 to get 90.

$$160x=90$$

Divide both sides by 160.

$$x=\frac{90}{160}$$

Reduce the fraction \frac{90}{160} to lowest terms by extracting and canceling out 10.

$$x=\frac{9}{16}$$