Solve 2x-1/3x+1-6x-2/3x+1=5/66)3x+2/2x-3+frac{1}{3}=frac{5x}{2}

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

Solve for x

$$x=-\frac{4}{19}\approx -0.210526316$$

Steps for Solving Linear Equation

Variable x cannot be equal to -\frac{1}{3} since division by zero is not defined. Multiply both sides of the equation by 6\left(3x+1\right), the least common multiple of 3x+1,6.

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

Use the distributive property to multiply 6 by 2x-1.

$$12x-6-6\left(6x-2\right)=\frac{5}{6}\times 6\times 6\left(3x+1\right)$$

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

$$12x-6-36x+12=\frac{5}{6}\times 6\times 6\left(3x+1\right)$$

Combine 12x and -36x to get -24x.

$$-24x-6+12=\frac{5}{6}\times 6\times 6\left(3x+1\right)$$

Add -6 and 12 to get 6.

$$-24x+6=\frac{5}{6}\times 6\times 6\left(3x+1\right)$$

Multiply \frac{5}{6} and 6 to get 5.

$$-24x+6=5\times 6\left(3x+1\right)$$

Multiply 5 and 6 to get 30.

$$-24x+6=30\left(3x+1\right)$$

Use the distributive property to multiply 30 by 3x+1.

$$-24x+6=90x+30$$

Subtract 90x from both sides.

$$-24x+6-90x=30$$

Combine -24x and -90x to get -114x.

$$-114x+6=30$$

Subtract 6 from both sides.

$$-114x=30-6$$

Subtract 6 from 30 to get 24.

$$-114x=24$$

Divide both sides by -114.

$$x=\frac{24}{-114}$$

Reduce the fraction \frac{24}{-114} to lowest terms by extracting and canceling out 6.

$$x=-\frac{4}{19}$$