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

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

Solve for x

$$x=\frac{10}{19}\approx 0.526315789$$

Steps for Solving Linear Equation

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

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

Multiply x and x to get x^{2}.

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

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

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

Subtract 1 from 3 to get 2.

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

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

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

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

$$12x^{2}-6+21x=12x^{2}-36x+24$$

Subtract 12x^{2} from both sides.

$$12x^{2}-6+21x-12x^{2}=-36x+24$$

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

$$-6+21x=-36x+24$$

Add 36x to both sides.

$$-6+21x+36x=24$$

Combine 21x and 36x to get 57x.

$$-6+57x=24$$

Add 6 to both sides.

$$57x=24+6$$

Add 24 and 6 to get 30.

$$57x=30$$

Divide both sides by 57.

$$x=\frac{30}{57}$$

Reduce the fraction \frac{30}{57} to lowest terms by extracting and canceling out 3.

$$x=\frac{10}{19}$$