Solve 3-x/3-2x-2/9=4-x/3

$$\frac { 3 - x } { 3 } - \frac { 2 x - 2 } { 9 } = 4 - \frac { x } { 3 }$$

Solve for x

$$x = -\frac{25}{2} = -12\frac{1}{2} = -12.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 9, the least common multiple of 3,9.

$$3\left(3-x\right)-\left(2x-2\right)=36-3x$$

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

$$9-3x-\left(2x-2\right)=36-3x$$

To find the opposite of 2x-2, find the opposite of each term.

$$9-3x-2x-\left(-2\right)=36-3x$$

The opposite of -2 is 2.

$$9-3x-2x+2=36-3x$$

Combine -3x and -2x to get -5x.

$$9-5x+2=36-3x$$

Add 9 and 2 to get 11.

$$11-5x=36-3x$$

Add 3x to both sides.

$$11-5x+3x=36$$

Combine -5x and 3x to get -2x.

$$11-2x=36$$

Subtract 11 from both sides.

$$-2x=36-11$$

Subtract 11 from 36 to get 25.

$$-2x=25$$

Divide both sides by -2.

$$x=\frac{25}{-2}$$

Fraction \frac{25}{-2} can be rewritten as -\frac{25}{2} by extracting the negative sign.

$$x=-\frac{25}{2}$$