Solve (0/10+x:5)*31/7-153/10=67/10*13frac{1}{3}-6frac{7}{10}*12frac{1}{3}

$$( \frac { 0 } { 10 } + x : 5 ) \cdot 3 \frac { 1 } { 7 } - 15 \frac { 3 } { 10 } = 6 \frac { 7 } { 10 } \cdot 13 \frac { 1 } { 3 } - 6 \frac { 7 } { 10 } \cdot 12 \frac { 1 } { 3 }$$

Solve for x

$$x=35$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 210, the least common multiple of 10,5,7,3.

$$30\left(\frac{0}{10}+\frac{x}{5}\right)\left(3\times 7+1\right)-21\left(15\times 10+3\right)=7\left(6\times 10+7\right)\left(13\times 3+1\right)-7\left(6\times 10+7\right)\left(12\times 3+1\right)$$

Zero divided by any non-zero number gives zero.

$$30\left(0+\frac{x}{5}\right)\left(3\times 7+1\right)-21\left(15\times 10+3\right)=7\left(6\times 10+7\right)\left(13\times 3+1\right)-7\left(6\times 10+7\right)\left(12\times 3+1\right)$$

Anything plus zero gives itself.

$$30\times \frac{x}{5}\left(3\times 7+1\right)-21\left(15\times 10+3\right)=7\left(6\times 10+7\right)\left(13\times 3+1\right)-7\left(6\times 10+7\right)\left(12\times 3+1\right)$$

Multiply 3 and 7 to get 21.

$$30\times \frac{x}{5}\left(21+1\right)-21\left(15\times 10+3\right)=7\left(6\times 10+7\right)\left(13\times 3+1\right)-7\left(6\times 10+7\right)\left(12\times 3+1\right)$$

Add 21 and 1 to get 22.

$$30\times \frac{x}{5}\times 22-21\left(15\times 10+3\right)=7\left(6\times 10+7\right)\left(13\times 3+1\right)-7\left(6\times 10+7\right)\left(12\times 3+1\right)$$

Multiply 30 and 22 to get 660.

$$660\times \frac{x}{5}-21\left(15\times 10+3\right)=7\left(6\times 10+7\right)\left(13\times 3+1\right)-7\left(6\times 10+7\right)\left(12\times 3+1\right)$$

Cancel out 5, the greatest common factor in 660 and 5.

$$132x-21\left(15\times 10+3\right)=7\left(6\times 10+7\right)\left(13\times 3+1\right)-7\left(6\times 10+7\right)\left(12\times 3+1\right)$$

Multiply 15 and 10 to get 150.

$$132x-21\left(150+3\right)=7\left(6\times 10+7\right)\left(13\times 3+1\right)-7\left(6\times 10+7\right)\left(12\times 3+1\right)$$

Add 150 and 3 to get 153.

$$132x-21\times 153=7\left(6\times 10+7\right)\left(13\times 3+1\right)-7\left(6\times 10+7\right)\left(12\times 3+1\right)$$

Multiply -21 and 153 to get -3213.

$$132x-3213=7\left(6\times 10+7\right)\left(13\times 3+1\right)-7\left(6\times 10+7\right)\left(12\times 3+1\right)$$

Multiply 6 and 10 to get 60.

$$132x-3213=7\left(60+7\right)\left(13\times 3+1\right)-7\left(6\times 10+7\right)\left(12\times 3+1\right)$$

Add 60 and 7 to get 67.

$$132x-3213=7\times 67\left(13\times 3+1\right)-7\left(6\times 10+7\right)\left(12\times 3+1\right)$$

Multiply 7 and 67 to get 469.

$$132x-3213=469\left(13\times 3+1\right)-7\left(6\times 10+7\right)\left(12\times 3+1\right)$$

Multiply 13 and 3 to get 39.

$$132x-3213=469\left(39+1\right)-7\left(6\times 10+7\right)\left(12\times 3+1\right)$$

Add 39 and 1 to get 40.

$$132x-3213=469\times 40-7\left(6\times 10+7\right)\left(12\times 3+1\right)$$

Multiply 469 and 40 to get 18760.

$$132x-3213=18760-7\left(6\times 10+7\right)\left(12\times 3+1\right)$$

Multiply 6 and 10 to get 60.

$$132x-3213=18760-7\left(60+7\right)\left(12\times 3+1\right)$$

Add 60 and 7 to get 67.

$$132x-3213=18760-7\times 67\left(12\times 3+1\right)$$

Multiply 7 and 67 to get 469.

$$132x-3213=18760-469\left(12\times 3+1\right)$$

Multiply 12 and 3 to get 36.

$$132x-3213=18760-469\left(36+1\right)$$

Add 36 and 1 to get 37.

$$132x-3213=18760-469\times 37$$

Multiply 469 and 37 to get 17353.

$$132x-3213=18760-17353$$

Subtract 17353 from 18760 to get 1407.

$$132x-3213=1407$$

Add 3213 to both sides.

$$132x=1407+3213$$

Add 1407 and 3213 to get 4620.

$$132x=4620$$

Divide both sides by 132.

$$x=\frac{4620}{132}$$

Divide 4620 by 132 to get 35.

$$x=35$$