Solve x+3/2+1/6=2x-4/3-3/4

$$\frac { x + 3 } { 2 } + \frac { 1 } { 6 } = \frac { 2 x - 4 } { 3 } - \frac { 3 } { 4 }$$

Solve for x

$$x = \frac{45}{2} = 22\frac{1}{2} = 22.5$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply 6 by x+3.

$$6x+18+2=4\left(2x-4\right)-9$$

Add 18 and 2 to get 20.

$$6x+20=4\left(2x-4\right)-9$$

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

$$6x+20=8x-16-9$$

Subtract 9 from -16 to get -25.

$$6x+20=8x-25$$

Subtract 8x from both sides.

$$6x+20-8x=-25$$

Combine 6x and -8x to get -2x.

$$-2x+20=-25$$

Subtract 20 from both sides.

$$-2x=-25-20$$

Subtract 20 from -25 to get -45.

$$-2x=-45$$

Divide both sides by -2.

$$x=\frac{-45}{-2}$$

Fraction \frac{-45}{-2} can be simplified to \frac{45}{2} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{45}{2}$$