Solve 2-7x/1-5x=3+7x/4+5x

$$\frac{ 2-7x }{ 1-5x } = \frac{ 3+7x }{ 4+5x }$$

Solve for x

$$x=\frac{1}{2}=0.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{4}{5},\frac{1}{5} since division by zero is not defined. Multiply both sides of the equation by \left(5x-1\right)\left(5x+4\right), the least common multiple of 1-5x,4+5x.

$$\left(-4-5x\right)\left(2-7x\right)=\left(5x-1\right)\left(3+7x\right)$$

Use the distributive property to multiply -4-5x by 2-7x and combine like terms.

$$-8+18x+35x^{2}=\left(5x-1\right)\left(3+7x\right)$$

Use the distributive property to multiply 5x-1 by 3+7x and combine like terms.

$$-8+18x+35x^{2}=8x+35x^{2}-3$$

Subtract 8x from both sides.

$$-8+18x+35x^{2}-8x=35x^{2}-3$$

Combine 18x and -8x to get 10x.

$$-8+10x+35x^{2}=35x^{2}-3$$

Subtract 35x^{2} from both sides.

$$-8+10x+35x^{2}-35x^{2}=-3$$

Combine 35x^{2} and -35x^{2} to get 0.

$$-8+10x=-3$$

Add 8 to both sides.

$$10x=-3+8$$

Add -3 and 8 to get 5.

$$10x=5$$

Divide both sides by 10.

$$x=\frac{5}{10}$$

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$x=\frac{1}{2}$$