Solve 2(3x+1)/15+x+5/3=3x-2/5-3(x+1)/15+frac{2}{5}

$$\frac { 2 ( 3 x + 1 ) } { 15 } + \frac { x + 5 } { 3 } = \frac { 3 x - 2 } { 5 } - \frac { 3 ( x + 1 ) } { 15 } + \frac { 2 } { 5 }$$

Solve for x

$$x=-6$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 15,3,5.

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

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

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

Use the distributive property to multiply 5 by x+5.

$$6x+2+5x+25=3\left(3x-2\right)-3\left(x+1\right)+6$$

Combine 6x and 5x to get 11x.

$$11x+2+25=3\left(3x-2\right)-3\left(x+1\right)+6$$

Add 2 and 25 to get 27.

$$11x+27=3\left(3x-2\right)-3\left(x+1\right)+6$$

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

$$11x+27=9x-6-3\left(x+1\right)+6$$

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

$$11x+27=9x-6-3x-3+6$$

Combine 9x and -3x to get 6x.

$$11x+27=6x-6-3+6$$

Subtract 3 from -6 to get -9.

$$11x+27=6x-9+6$$

Add -9 and 6 to get -3.

$$11x+27=6x-3$$

Subtract 6x from both sides.

$$11x+27-6x=-3$$

Combine 11x and -6x to get 5x.

$$5x+27=-3$$

Subtract 27 from both sides.

$$5x=-3-27$$

Subtract 27 from -3 to get -30.

$$5x=-30$$

Divide both sides by 5.

$$x=\frac{-30}{5}$$

Divide -30 by 5 to get -6.

$$x=-6$$