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

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

Solve for z

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

Steps for Solving Linear Equation

Variable z 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(5z-1\right)\left(5z+4\right), the least common multiple of 1-5z,4+5z.

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

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

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

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

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

Subtract 8z from both sides.

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

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

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

Subtract 35z^{2} from both sides.

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

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

$$-8+10z=-3$$

Add 8 to both sides.

$$10z=-3+8$$

Add -3 and 8 to get 5.

$$10z=5$$

Divide both sides by 10.

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

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

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