Solve 1-2x-3/36=3x-2+x/5-x-1/6

$$\frac { 1 - 2 x - 3 } { 36 } = 3 x - \frac { 2 + x } { 5 } - \frac { x - 1 } { 6 }$$

Solve for x

$$x=\frac{8}{121}\approx 0.066115702$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 180, the least common multiple of 36,5,6.

$$5\left(1-2x-3\right)=540x-36\left(2+x\right)-30\left(x-1\right)$$

Subtract 3 from 1 to get -2.

$$5\left(-2-2x\right)=540x-36\left(2+x\right)-30\left(x-1\right)$$

Use the distributive property to multiply 5 by -2-2x.

$$-10-10x=540x-36\left(2+x\right)-30\left(x-1\right)$$

Use the distributive property to multiply -36 by 2+x.

$$-10-10x=540x-72-36x-30\left(x-1\right)$$

Combine 540x and -36x to get 504x.

$$-10-10x=504x-72-30\left(x-1\right)$$

Use the distributive property to multiply -30 by x-1.

$$-10-10x=504x-72-30x+30$$

Combine 504x and -30x to get 474x.

$$-10-10x=474x-72+30$$

Add -72 and 30 to get -42.

$$-10-10x=474x-42$$

Subtract 474x from both sides.

$$-10-10x-474x=-42$$

Combine -10x and -474x to get -484x.

$$-10-484x=-42$$

Add 10 to both sides.

$$-484x=-42+10$$

Add -42 and 10 to get -32.

$$-484x=-32$$

Divide both sides by -484.

$$x=\frac{-32}{-484}$$

Reduce the fraction \frac{-32}{-484} to lowest terms by extracting and canceling out -4.

$$x=\frac{8}{121}$$