Solve ((1/2+1)^4:(5/4+3/8-1/16)):(frac{11}{8}+frac{7}{40}+frac{1}{5})=x:(1-frac{2}{3}+frac{1}{4}-frac{1}{6})

$$( ( \frac { 1 } { 2 } + 1 ) ^ { 4 } : ( \frac { 5 } { 4 } + \frac { 3 } { 8 } - \frac { 1 } { 16 } ) ) : ( \frac { 11 } { 8 } + \frac { 7 } { 40 } + \frac { 1 } { 5 } ) = x : ( 1 - \frac { 2 } { 3 } + \frac { 1 } { 4 } - \frac { 1 } { 6 } )$$

Solve for x

$$x=\frac{27}{35}\approx 0.771428571$$

Steps for Solving Linear Equation

Add \frac{1}{2} and 1 to get \frac{3}{2}.

$$\frac{\frac{\left(\frac{3}{2}\right)^{4}}{\frac{5}{4}+\frac{3}{8}-\frac{1}{16}}}{\frac{11}{8}+\frac{7}{40}+\frac{1}{5}}=\frac{x}{1-\frac{2}{3}+\frac{1}{4}-\frac{1}{6}}$$

Calculate \frac{3}{2} to the power of 4 and get \frac{81}{16}.

$$\frac{\frac{\frac{81}{16}}{\frac{5}{4}+\frac{3}{8}-\frac{1}{16}}}{\frac{11}{8}+\frac{7}{40}+\frac{1}{5}}=\frac{x}{1-\frac{2}{3}+\frac{1}{4}-\frac{1}{6}}$$

Add \frac{5}{4} and \frac{3}{8} to get \frac{13}{8}.

$$\frac{\frac{\frac{81}{16}}{\frac{13}{8}-\frac{1}{16}}}{\frac{11}{8}+\frac{7}{40}+\frac{1}{5}}=\frac{x}{1-\frac{2}{3}+\frac{1}{4}-\frac{1}{6}}$$

Subtract \frac{1}{16} from \frac{13}{8} to get \frac{25}{16}.

$$\frac{\frac{\frac{81}{16}}{\frac{25}{16}}}{\frac{11}{8}+\frac{7}{40}+\frac{1}{5}}=\frac{x}{1-\frac{2}{3}+\frac{1}{4}-\frac{1}{6}}$$

Divide \frac{81}{16} by \frac{25}{16} by multiplying \frac{81}{16} by the reciprocal of \frac{25}{16}.

$$\frac{\frac{81}{16}\times \frac{16}{25}}{\frac{11}{8}+\frac{7}{40}+\frac{1}{5}}=\frac{x}{1-\frac{2}{3}+\frac{1}{4}-\frac{1}{6}}$$

Multiply \frac{81}{16} and \frac{16}{25} to get \frac{81}{25}.

$$\frac{\frac{81}{25}}{\frac{11}{8}+\frac{7}{40}+\frac{1}{5}}=\frac{x}{1-\frac{2}{3}+\frac{1}{4}-\frac{1}{6}}$$

Add \frac{11}{8} and \frac{7}{40} to get \frac{31}{20}.

$$\frac{\frac{81}{25}}{\frac{31}{20}+\frac{1}{5}}=\frac{x}{1-\frac{2}{3}+\frac{1}{4}-\frac{1}{6}}$$

Add \frac{31}{20} and \frac{1}{5} to get \frac{7}{4}.

$$\frac{\frac{81}{25}}{\frac{7}{4}}=\frac{x}{1-\frac{2}{3}+\frac{1}{4}-\frac{1}{6}}$$

Divide \frac{81}{25} by \frac{7}{4} by multiplying \frac{81}{25} by the reciprocal of \frac{7}{4}.

$$\frac{81}{25}\times \frac{4}{7}=\frac{x}{1-\frac{2}{3}+\frac{1}{4}-\frac{1}{6}}$$

Multiply \frac{81}{25} and \frac{4}{7} to get \frac{324}{175}.

$$\frac{324}{175}=\frac{x}{1-\frac{2}{3}+\frac{1}{4}-\frac{1}{6}}$$

Subtract \frac{2}{3} from 1 to get \frac{1}{3}.

$$\frac{324}{175}=\frac{x}{\frac{1}{3}+\frac{1}{4}-\frac{1}{6}}$$

Add \frac{1}{3} and \frac{1}{4} to get \frac{7}{12}.

$$\frac{324}{175}=\frac{x}{\frac{7}{12}-\frac{1}{6}}$$

Subtract \frac{1}{6} from \frac{7}{12} to get \frac{5}{12}.

$$\frac{324}{175}=\frac{x}{\frac{5}{12}}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{x}{\frac{5}{12}}=\frac{324}{175}$$

Multiply both sides by \frac{5}{12}.

$$x=\frac{324}{175}\times \frac{5}{12}$$

Multiply \frac{324}{175} and \frac{5}{12} to get \frac{27}{35}.

$$x=\frac{27}{35}$$