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

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

Solve for x

$$x = -\frac{23}{5} = -4\frac{3}{5} = -4.6$$

Steps for Solving Linear Equation

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

$$3\left(3x+9\right)-2\left(2x-4\right)=12$$

Use the distributive property to multiply 3 by 3x+9.

$$9x+27-2\left(2x-4\right)=12$$

Use the distributive property to multiply -2 by 2x-4.

$$9x+27-4x+8=12$$

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

$$5x+27+8=12$$

Add 27 and 8 to get 35.

$$5x+35=12$$

Subtract 35 from both sides.

$$5x=12-35$$

Subtract 35 from 12 to get -23.

$$5x=-23$$

Divide both sides by 5.

$$x=\frac{-23}{5}$$

Fraction \frac{-23}{5} can be rewritten as -\frac{23}{5} by extracting the negative sign.

$$x=-\frac{23}{5}$$