Solve 5x-16/6=-x+8/12+x+1/3

$$\frac { 5 x - 16 } { 6 } = - \frac { x + 8 } { 12 } + \frac { x + 1 } { 3 }$$

Solve for x

$$x=4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 6,12,3.

$$2\left(5x-16\right)=-\left(x+8\right)+4\left(x+1\right)$$

Use the distributive property to multiply 2 by 5x-16.

$$10x-32=-\left(x+8\right)+4\left(x+1\right)$$

To find the opposite of x+8, find the opposite of each term.

$$10x-32=-x-8+4\left(x+1\right)$$

Use the distributive property to multiply 4 by x+1.

$$10x-32=-x-8+4x+4$$

Combine -x and 4x to get 3x.

$$10x-32=3x-8+4$$

Add -8 and 4 to get -4.

$$10x-32=3x-4$$

Subtract 3x from both sides.

$$10x-32-3x=-4$$

Combine 10x and -3x to get 7x.

$$7x-32=-4$$

Add 32 to both sides.

$$7x=-4+32$$

Add -4 and 32 to get 28.

$$7x=28$$

Divide both sides by 7.

$$x=\frac{28}{7}$$

Divide 28 by 7 to get 4.

$$x=4$$