Solve 6x(x-1/3)-1/2[3-(7x+1)]=2x(x-3)+4

$$6 x ( \frac { x - 1 } { 3 } ) - \frac { 1 } { 2 } [ 3 - ( 7 x + 1 ) ] = 2 x ( x - 3 ) + 4$$

Solve for x

$$x=\frac{2}{3}\approx 0.666666667$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$12x\left(x-1\right)-3\left(3-\left(7x+1\right)\right)=12x\left(x-3\right)+24$$

Use the distributive property to multiply 12x by x-1.

$$12x^{2}-12x-3\left(3-\left(7x+1\right)\right)=12x\left(x-3\right)+24$$

To find the opposite of 7x+1, find the opposite of each term.

$$12x^{2}-12x-3\left(3-7x-1\right)=12x\left(x-3\right)+24$$

Subtract 1 from 3 to get 2.

$$12x^{2}-12x-3\left(2-7x\right)=12x\left(x-3\right)+24$$

Use the distributive property to multiply -3 by 2-7x.

$$12x^{2}-12x-6+21x=12x\left(x-3\right)+24$$

Combine -12x and 21x to get 9x.

$$12x^{2}+9x-6=12x\left(x-3\right)+24$$

Use the distributive property to multiply 12x by x-3.

$$12x^{2}+9x-6=12x^{2}-36x+24$$

Subtract 12x^{2} from both sides.

$$12x^{2}+9x-6-12x^{2}=-36x+24$$

Combine 12x^{2} and -12x^{2} to get 0.

$$9x-6=-36x+24$$

Add 36x to both sides.

$$9x-6+36x=24$$

Combine 9x and 36x to get 45x.

$$45x-6=24$$

Add 6 to both sides.

$$45x=24+6$$

Add 24 and 6 to get 30.

$$45x=30$$

Divide both sides by 45.

$$x=\frac{30}{45}$$

Reduce the fraction \frac{30}{45} to lowest terms by extracting and canceling out 15.

$$x=\frac{2}{3}$$