Solve (x-4):(20+1/4)=(2/3)^2:(1+2)

$$( x - 4 ) : ( 20 + \frac { 1 } { 4 } ) = ( \frac { 2 } { 3 } ) ^ { 2 } : ( 1 + 2 )$$

Solve for x

$$x=7$$

Steps for Solving Linear Equation

Convert 20 to fraction \frac{80}{4}.

$$\frac{x-4}{\frac{80}{4}+\frac{1}{4}}=\frac{\left(\frac{2}{3}\right)^{2}}{1+2}$$

Since \frac{80}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{x-4}{\frac{80+1}{4}}=\frac{\left(\frac{2}{3}\right)^{2}}{1+2}$$

Add 80 and 1 to get 81.

$$\frac{x-4}{\frac{81}{4}}=\frac{\left(\frac{2}{3}\right)^{2}}{1+2}$$

Calculate \frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$\frac{x-4}{\frac{81}{4}}=\frac{\frac{4}{9}}{1+2}$$

Add 1 and 2 to get 3.

$$\frac{x-4}{\frac{81}{4}}=\frac{\frac{4}{9}}{3}$$

Express \frac{\frac{4}{9}}{3} as a single fraction.

$$\frac{x-4}{\frac{81}{4}}=\frac{4}{9\times 3}$$

Multiply 9 and 3 to get 27.

$$\frac{x-4}{\frac{81}{4}}=\frac{4}{27}$$

Divide each term of x-4 by \frac{81}{4} to get \frac{x}{\frac{81}{4}}+\frac{-4}{\frac{81}{4}}.

$$\frac{x}{\frac{81}{4}}+\frac{-4}{\frac{81}{4}}=\frac{4}{27}$$

Divide -4 by \frac{81}{4} by multiplying -4 by the reciprocal of \frac{81}{4}.

$$\frac{x}{\frac{81}{4}}-4\times \frac{4}{81}=\frac{4}{27}$$

Express -4\times \frac{4}{81} as a single fraction.

$$\frac{x}{\frac{81}{4}}+\frac{-4\times 4}{81}=\frac{4}{27}$$

Multiply -4 and 4 to get -16.

$$\frac{x}{\frac{81}{4}}+\frac{-16}{81}=\frac{4}{27}$$

Fraction \frac{-16}{81} can be rewritten as -\frac{16}{81} by extracting the negative sign.

$$\frac{x}{\frac{81}{4}}-\frac{16}{81}=\frac{4}{27}$$

Add \frac{16}{81} to both sides.

$$\frac{x}{\frac{81}{4}}=\frac{4}{27}+\frac{16}{81}$$

Least common multiple of 27 and 81 is 81. Convert \frac{4}{27} and \frac{16}{81} to fractions with denominator 81.

$$\frac{x}{\frac{81}{4}}=\frac{12}{81}+\frac{16}{81}$$

Since \frac{12}{81} and \frac{16}{81} have the same denominator, add them by adding their numerators.

$$\frac{x}{\frac{81}{4}}=\frac{12+16}{81}$$

Add 12 and 16 to get 28.

$$\frac{x}{\frac{81}{4}}=\frac{28}{81}$$

Multiply both sides by \frac{81}{4}.

$$x=\frac{28}{81}\times \frac{81}{4}$$

Multiply \frac{28}{81} times \frac{81}{4} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{28\times 81}{81\times 4}$$

Cancel out 81 in both numerator and denominator.

$$x=\frac{28}{4}$$

Divide 28 by 4 to get 7.

$$x=7$$