Solve x-5(1-x)/2-2-3(1-2x)/6=0

$$x - \frac { 5 ( 1 - x ) } { 2 } - \frac { 2 - 3 ( 1 - 2 x ) } { 6 } = 0$$

Solve for x

$$x=\frac{14}{15}\approx 0.933333333$$

Steps for Solving Linear Equation

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

$$6x-3\times 5\left(1-x\right)-\left(2-3\left(1-2x\right)\right)=0$$

Multiply -3 and 5 to get -15.

$$6x-15\left(1-x\right)-\left(2-3\left(1-2x\right)\right)=0$$

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

$$6x-15+15x-\left(2-3\left(1-2x\right)\right)=0$$

Combine 6x and 15x to get 21x.

$$21x-15-\left(2-3\left(1-2x\right)\right)=0$$

Use the distributive property to multiply -3 by 1-2x.

$$21x-15-\left(2-3+6x\right)=0$$

Subtract 3 from 2 to get -1.

$$21x-15-\left(-1+6x\right)=0$$

To find the opposite of -1+6x, find the opposite of each term.

$$21x-15-\left(-1\right)-6x=0$$

The opposite of -1 is 1.

$$21x-15+1-6x=0$$

Add -15 and 1 to get -14.

$$21x-14-6x=0$$

Combine 21x and -6x to get 15x.

$$15x-14=0$$

Add 14 to both sides. Anything plus zero gives itself.

$$15x=14$$

Divide both sides by 15.

$$x=\frac{14}{15}$$