Solve x-4/3+2x-3/4=3x/2-2x-3/6

$$\frac{ x-4 }{ 3 } + \frac{ 2x-3 }{ 4 } = \frac{ 3x }{ 2 } - \frac{ 2x-3 }{ 6 }$$

Solve for x

$$x = -\frac{31}{4} = -7\frac{3}{4} = -7.75$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 3,4,2,6.

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

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

$$4x-16+3\left(2x-3\right)=6\times 3x-2\left(2x-3\right)$$

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

$$4x-16+6x-9=6\times 3x-2\left(2x-3\right)$$

Combine 4x and 6x to get 10x.

$$10x-16-9=6\times 3x-2\left(2x-3\right)$$

Subtract 9 from -16 to get -25.

$$10x-25=6\times 3x-2\left(2x-3\right)$$

Multiply 6 and 3 to get 18.

$$10x-25=18x-2\left(2x-3\right)$$

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

$$10x-25=18x-4x+6$$

Combine 18x and -4x to get 14x.

$$10x-25=14x+6$$

Subtract 14x from both sides.

$$10x-25-14x=6$$

Combine 10x and -14x to get -4x.

$$-4x-25=6$$

Add 25 to both sides.

$$-4x=6+25$$

Add 6 and 25 to get 31.

$$-4x=31$$

Divide both sides by -4.

$$x=\frac{31}{-4}$$

Fraction \frac{31}{-4} can be rewritten as -\frac{31}{4} by extracting the negative sign.

$$x=-\frac{31}{4}$$