Solve 43/13left(x-12/7right)=x*21/7-43/15x

$$4 \frac{ 3 }{ 13 } \left( x-1 \frac{ 2 }{ 7 } \right) = x \times 2 \frac{ 1 }{ 7 } -4 \frac{ 3 }{ 15 } x$$

Solve for x

$$x=\frac{2475}{2861}\approx 0.865082139$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 1365, the least common multiple of 13,7,15.

$$105\left(4\times 13+3\right)\left(x-\frac{1\times 7+2}{7}\right)=195x\left(2\times 7+1\right)-91\left(4\times 15+3\right)x$$

Multiply 4 and 13 to get 52.

$$105\left(52+3\right)\left(x-\frac{1\times 7+2}{7}\right)=195x\left(2\times 7+1\right)-91\left(4\times 15+3\right)x$$

Add 52 and 3 to get 55.

$$105\times 55\left(x-\frac{1\times 7+2}{7}\right)=195x\left(2\times 7+1\right)-91\left(4\times 15+3\right)x$$

Multiply 105 and 55 to get 5775.

$$5775\left(x-\frac{1\times 7+2}{7}\right)=195x\left(2\times 7+1\right)-91\left(4\times 15+3\right)x$$

Multiply 1 and 7 to get 7.

$$5775\left(x-\frac{7+2}{7}\right)=195x\left(2\times 7+1\right)-91\left(4\times 15+3\right)x$$

Add 7 and 2 to get 9.

$$5775\left(x-\frac{9}{7}\right)=195x\left(2\times 7+1\right)-91\left(4\times 15+3\right)x$$

Use the distributive property to multiply 5775 by x-\frac{9}{7}.

$$5775x+5775\left(-\frac{9}{7}\right)=195x\left(2\times 7+1\right)-91\left(4\times 15+3\right)x$$

Express 5775\left(-\frac{9}{7}\right) as a single fraction.

$$5775x+\frac{5775\left(-9\right)}{7}=195x\left(2\times 7+1\right)-91\left(4\times 15+3\right)x$$

Multiply 5775 and -9 to get -51975.

$$5775x+\frac{-51975}{7}=195x\left(2\times 7+1\right)-91\left(4\times 15+3\right)x$$

Divide -51975 by 7 to get -7425.

$$5775x-7425=195x\left(2\times 7+1\right)-91\left(4\times 15+3\right)x$$

Multiply 2 and 7 to get 14.

$$5775x-7425=195x\left(14+1\right)-91\left(4\times 15+3\right)x$$

Add 14 and 1 to get 15.

$$5775x-7425=195x\times 15-91\left(4\times 15+3\right)x$$

Multiply 195 and 15 to get 2925.

$$5775x-7425=2925x-91\left(4\times 15+3\right)x$$

Multiply 4 and 15 to get 60.

$$5775x-7425=2925x-91\left(60+3\right)x$$

Add 60 and 3 to get 63.

$$5775x-7425=2925x-91\times 63x$$

Multiply 91 and 63 to get 5733.

$$5775x-7425=2925x-5733x$$

Combine 2925x and -5733x to get -2808x.

$$5775x-7425=-2808x$$

Add 2808x to both sides.

$$5775x-7425+2808x=0$$

Combine 5775x and 2808x to get 8583x.

$$8583x-7425=0$$

Add 7425 to both sides. Anything plus zero gives itself.

$$8583x=7425$$

Divide both sides by 8583.

$$x=\frac{7425}{8583}$$

Reduce the fraction \frac{7425}{8583} to lowest terms by extracting and canceling out 3.

$$x=\frac{2475}{2861}$$