Solve 3(x-1)-2x/5=5(x-3)/6

$$\frac{ 3(x-1)-2x }{ 5 } = \frac{ 5(x-3) }{ 6 }$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 5,6.

$$6\left(3\left(x-1\right)-2x\right)=5\times 5\left(x-3\right)$$

Use the distributive property to multiply 3 by x-1.

$$6\left(3x-3-2x\right)=5\times 5\left(x-3\right)$$

Combine 3x and -2x to get x.

$$6\left(x-3\right)=5\times 5\left(x-3\right)$$

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

$$6x-18=5\times 5\left(x-3\right)$$

Multiply 5 and 5 to get 25.

$$6x-18=25\left(x-3\right)$$

Use the distributive property to multiply 25 by x-3.

$$6x-18=25x-75$$

Subtract 25x from both sides.

$$6x-18-25x=-75$$

Combine 6x and -25x to get -19x.

$$-19x-18=-75$$

Add 18 to both sides.

$$-19x=-75+18$$

Add -75 and 18 to get -57.

$$-19x=-57$$

Divide both sides by -19.

$$x=\frac{-57}{-19}$$

Divide -57 by -19 to get 3.

$$x=3$$