Solve x+2(x-3)/3=6-x-7/6

$$x + \frac { 2 ( x - 3 ) } { 3 } = 6 - \frac { x - 7 } { 6 }$$

Solve for x

$$x=5$$

Steps for Solving Linear Equation

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

$$6x+2\times 2\left(x-3\right)=36-\left(x-7\right)$$

Multiply 2 and 2 to get 4.

$$6x+4\left(x-3\right)=36-\left(x-7\right)$$

Use the distributive property to multiply 4 by x-3.

$$6x+4x-12=36-\left(x-7\right)$$

Combine 6x and 4x to get 10x.

$$10x-12=36-\left(x-7\right)$$

To find the opposite of x-7, find the opposite of each term.

$$10x-12=36-x-\left(-7\right)$$

The opposite of -7 is 7.

$$10x-12=36-x+7$$

Add 36 and 7 to get 43.

$$10x-12=43-x$$

Add x to both sides.

$$10x-12+x=43$$

Combine 10x and x to get 11x.

$$11x-12=43$$

Add 12 to both sides.

$$11x=43+12$$

Add 43 and 12 to get 55.

$$11x=55$$

Divide both sides by 11.

$$x=\frac{55}{11}$$

Divide 55 by 11 to get 5.

$$x=5$$