Solve 11/2frac{3{6}}+25/6=3x/8-3

$$1 \frac { 1 } { 2 \frac { 3 } { 6 } } + 2 \frac { 5 } { 6 } = 3 \frac { x } { 8 } - 3$$

Solve for x

$$x = \frac{748}{45} = 16\frac{28}{45} \approx 16.622222222$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 24, the least common multiple of 6,8.

$$24\times \frac{1}{\frac{2\times 6+3}{6}}+4\left(2\times 6+5\right)=9x-72$$

Divide 1 by \frac{2\times 6+3}{6} by multiplying 1 by the reciprocal of \frac{2\times 6+3}{6}.

$$24\times \frac{6}{2\times 6+3}+4\left(2\times 6+5\right)=9x-72$$

Multiply 2 and 6 to get 12.

$$24\times \frac{6}{12+3}+4\left(2\times 6+5\right)=9x-72$$

Add 12 and 3 to get 15.

$$24\times \frac{6}{15}+4\left(2\times 6+5\right)=9x-72$$

Reduce the fraction \frac{6}{15} to lowest terms by extracting and canceling out 3.

$$24\times \frac{2}{5}+4\left(2\times 6+5\right)=9x-72$$

Express 24\times \frac{2}{5} as a single fraction.

$$\frac{24\times 2}{5}+4\left(2\times 6+5\right)=9x-72$$

Multiply 24 and 2 to get 48.

$$\frac{48}{5}+4\left(2\times 6+5\right)=9x-72$$

Multiply 2 and 6 to get 12.

$$\frac{48}{5}+4\left(12+5\right)=9x-72$$

Add 12 and 5 to get 17.

$$\frac{48}{5}+4\times 17=9x-72$$

Multiply 4 and 17 to get 68.

$$\frac{48}{5}+68=9x-72$$

Convert 68 to fraction \frac{340}{5}.

$$\frac{48}{5}+\frac{340}{5}=9x-72$$

Since \frac{48}{5} and \frac{340}{5} have the same denominator, add them by adding their numerators.

$$\frac{48+340}{5}=9x-72$$

Add 48 and 340 to get 388.

$$\frac{388}{5}=9x-72$$

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

$$9x-72=\frac{388}{5}$$

Add 72 to both sides.

$$9x=\frac{388}{5}+72$$

Convert 72 to fraction \frac{360}{5}.

$$9x=\frac{388}{5}+\frac{360}{5}$$

Since \frac{388}{5} and \frac{360}{5} have the same denominator, add them by adding their numerators.

$$9x=\frac{388+360}{5}$$

Add 388 and 360 to get 748.

$$9x=\frac{748}{5}$$

Divide both sides by 9.

$$x=\frac{\frac{748}{5}}{9}$$

Express \frac{\frac{748}{5}}{9} as a single fraction.

$$x=\frac{748}{5\times 9}$$

Multiply 5 and 9 to get 45.

$$x=\frac{748}{45}$$