Solve z-6/4-z-7/6=z-4/12

$$\frac { z - 6 } { 4 } - \frac { z - 7 } { 6 } = \frac { z - 4 } { 12 }$$

Solve for z

$$z\in \mathrm{R}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 4,6,12.

$$3\left(z-6\right)-2\left(z-7\right)=z-4$$

Use the distributive property to multiply 3 by z-6.

$$3z-18-2\left(z-7\right)=z-4$$

Use the distributive property to multiply -2 by z-7.

$$3z-18-2z+14=z-4$$

Combine 3z and -2z to get z.

$$z-18+14=z-4$$

Add -18 and 14 to get -4.

$$z-4=z-4$$

Subtract z from both sides.

$$z-4-z=-4$$

Combine z and -z to get 0.

$$-4=-4$$

Compare -4 and -4.

$$\text{true}$$

This is true for any z.

$$z\in \mathrm{R}$$