Solve 2x+(3x-9)/4=-2x+20/6+2x-3

$$\frac { 2 x + ( 3 x - 9 ) } { 4 } = \frac { - 2 x + 20 } { 6 } + 2 x - 3$$

Solve for x

$$x = -\frac{31}{5} = -6\frac{1}{5} = -6.2$$

Steps for Solving Linear Equation

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

$$3\left(2x+3x-9\right)=2\left(-2x+20\right)+24x-36$$

Combine 2x and 3x to get 5x.

$$3\left(5x-9\right)=2\left(-2x+20\right)+24x-36$$

Use the distributive property to multiply 3 by 5x-9.

$$15x-27=2\left(-2x+20\right)+24x-36$$

Use the distributive property to multiply 2 by -2x+20.

$$15x-27=-4x+40+24x-36$$

Combine -4x and 24x to get 20x.

$$15x-27=20x+40-36$$

Subtract 36 from 40 to get 4.

$$15x-27=20x+4$$

Subtract 20x from both sides.

$$15x-27-20x=4$$

Combine 15x and -20x to get -5x.

$$-5x-27=4$$

Add 27 to both sides.

$$-5x=4+27$$

Add 4 and 27 to get 31.

$$-5x=31$$

Divide both sides by -5.

$$x=\frac{31}{-5}$$

Fraction \frac{31}{-5} can be rewritten as -\frac{31}{5} by extracting the negative sign.

$$x=-\frac{31}{5}$$