Solve 2z/-3z/2+5z/6=-4/9z+3

$$\frac{ 2z }{ } - \frac{ 3z }{ 2 } + \frac{ 5z }{ 6 } = - \frac{ 4 }{ 9 } z+3$$

Solve for z

$$z = \frac{27}{16} = 1\frac{11}{16} = 1.6875$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 18, the least common multiple of 2,6,9.

$$18\times 2z-9\times 3z+3\times 5z=-8z+54$$

Multiply 18 and 2 to get 36.

$$36z-9\times 3z+3\times 5z=-8z+54$$

Multiply -9 and 3 to get -27.

$$36z-27z+3\times 5z=-8z+54$$

Combine 36z and -27z to get 9z.

$$9z+3\times 5z=-8z+54$$

Multiply 3 and 5 to get 15.

$$9z+15z=-8z+54$$

Combine 9z and 15z to get 24z.

$$24z=-8z+54$$

Add 8z to both sides.

$$24z+8z=54$$

Combine 24z and 8z to get 32z.

$$32z=54$$

Divide both sides by 32.

$$z=\frac{54}{32}$$

Reduce the fraction \frac{54}{32} to lowest terms by extracting and canceling out 2.

$$z=\frac{27}{16}$$