Solve x+3/2+3x-6/3-9-x/6=1

$$\frac{ x+3 }{ 2 } + \frac{ 3x-6 }{ 3 } - \frac{ 9-x }{ 6 } =1$$

Solve for x

$$x = \frac{9}{5} = 1\frac{4}{5} = 1.8$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3,6.

$$3\left(x+3\right)+2\left(3x-6\right)-\left(9-x\right)=6$$

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

$$3x+9+2\left(3x-6\right)-\left(9-x\right)=6$$

Use the distributive property to multiply 2 by 3x-6.

$$3x+9+6x-12-\left(9-x\right)=6$$

Combine 3x and 6x to get 9x.

$$9x+9-12-\left(9-x\right)=6$$

Subtract 12 from 9 to get -3.

$$9x-3-\left(9-x\right)=6$$

To find the opposite of 9-x, find the opposite of each term.

$$9x-3-9-\left(-x\right)=6$$

The opposite of -x is x.

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

Subtract 9 from -3 to get -12.

$$9x-12+x=6$$

Combine 9x and x to get 10x.

$$10x-12=6$$

Add 12 to both sides.

$$10x=6+12$$

Add 6 and 12 to get 18.

$$10x=18$$

Divide both sides by 10.

$$x=\frac{18}{10}$$

Reduce the fraction \frac{18}{10} to lowest terms by extracting and canceling out 2.

$$x=\frac{9}{5}$$