Solve 5+x/5+2x+1/10-6x/5=-x/6+frac{3x+1}{6}

$$\frac { 5 + x } { 5 } + \frac { 2 x + 1 } { 10 } - \frac { 6 x } { 5 } = - \frac { x } { 6 } + \frac { 3 x + 1 } { 6 }$$

Solve for x

$$x=\frac{14}{17}\approx 0.823529412$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 5,10,6.

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

Use the distributive property to multiply 6 by 5+x.

$$30+6x+3\left(2x+1\right)-6\times 6x=-5x+5\left(3x+1\right)$$

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

$$30+6x+6x+3-6\times 6x=-5x+5\left(3x+1\right)$$

Combine 6x and 6x to get 12x.

$$30+12x+3-6\times 6x=-5x+5\left(3x+1\right)$$

Add 30 and 3 to get 33.

$$33+12x-6\times 6x=-5x+5\left(3x+1\right)$$

Multiply -6 and 6 to get -36.

$$33+12x-36x=-5x+5\left(3x+1\right)$$

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

$$33-24x=-5x+5\left(3x+1\right)$$

Use the distributive property to multiply 5 by 3x+1.

$$33-24x=-5x+15x+5$$

Combine -5x and 15x to get 10x.

$$33-24x=10x+5$$

Subtract 10x from both sides.

$$33-24x-10x=5$$

Combine -24x and -10x to get -34x.

$$33-34x=5$$

Subtract 33 from both sides.

$$-34x=5-33$$

Subtract 33 from 5 to get -28.

$$-34x=-28$$

Divide both sides by -34.

$$x=\frac{-28}{-34}$$

Reduce the fraction \frac{-28}{-34} to lowest terms by extracting and canceling out -2.

$$x=\frac{14}{17}$$