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

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

Solve for x

$$x = -\frac{24}{5} = -4\frac{4}{5} = -4.8$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 2,3,4.

$$6\left(2x-3\right)-12x=4\left(3-x\right)+3\left(3x-2\right)$$

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

$$12x-18-12x=4\left(3-x\right)+3\left(3x-2\right)$$

Combine 12x and -12x to get 0.

$$-18=4\left(3-x\right)+3\left(3x-2\right)$$

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

$$-18=12-4x+3\left(3x-2\right)$$

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

$$-18=12-4x+9x-6$$

Combine -4x and 9x to get 5x.

$$-18=12+5x-6$$

Subtract 6 from 12 to get 6.

$$-18=6+5x$$

Swap sides so that all variable terms are on the left hand side.

$$6+5x=-18$$

Subtract 6 from both sides.

$$5x=-18-6$$

Subtract 6 from -18 to get -24.

$$5x=-24$$

Divide both sides by 5.

$$x=\frac{-24}{5}$$

Fraction \frac{-24}{5} can be rewritten as -\frac{24}{5} by extracting the negative sign.

$$x=-\frac{24}{5}$$