Solve +2x-3/5+3(x-1)/6=2(x-3)/15+x

$$+ \frac { 2 x - 3 } { 5 } + \frac { 3 ( x - 1 ) } { 6 } = \frac { 2 ( x - 3 ) } { 15 } + x$$

Solve for x

$$x=-3$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 5,6,15.

$$6\left(2x-3\right)+5\times 3\left(x-1\right)=2\times 2\left(x-3\right)+30x$$

Use the distributive property to multiply 6 by 2x-3.

$$12x-18+5\times 3\left(x-1\right)=2\times 2\left(x-3\right)+30x$$

Multiply 5 and 3 to get 15.

$$12x-18+15\left(x-1\right)=2\times 2\left(x-3\right)+30x$$

Use the distributive property to multiply 15 by x-1.

$$12x-18+15x-15=2\times 2\left(x-3\right)+30x$$

Combine 12x and 15x to get 27x.

$$27x-18-15=2\times 2\left(x-3\right)+30x$$

Subtract 15 from -18 to get -33.

$$27x-33=2\times 2\left(x-3\right)+30x$$

Multiply 2 and 2 to get 4.

$$27x-33=4\left(x-3\right)+30x$$

Use the distributive property to multiply 4 by x-3.

$$27x-33=4x-12+30x$$

Combine 4x and 30x to get 34x.

$$27x-33=34x-12$$

Subtract 34x from both sides.

$$27x-33-34x=-12$$

Combine 27x and -34x to get -7x.

$$-7x-33=-12$$

Add 33 to both sides.

$$-7x=-12+33$$

Add -12 and 33 to get 21.

$$-7x=21$$

Divide both sides by -7.

$$x=\frac{21}{-7}$$

Divide 21 by -7 to get -3.

$$x=-3$$