Solve x+3/2-3x+1/4=2(x-2)-2/3

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

Solve for x

$$x = \frac{39}{11} = 3\frac{6}{11} \approx 3.545454545$$

Steps for Solving Linear Equation

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

$$6\left(x+3\right)-3\left(3x+1\right)=4\left(2\left(x-2\right)-2\right)$$

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

$$6x+18-3\left(3x+1\right)=4\left(2\left(x-2\right)-2\right)$$

Use the distributive property to multiply -3 by 3x+1.

$$6x+18-9x-3=4\left(2\left(x-2\right)-2\right)$$

Combine 6x and -9x to get -3x.

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

Subtract 3 from 18 to get 15.

$$-3x+15=4\left(2\left(x-2\right)-2\right)$$

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

$$-3x+15=4\left(2x-4-2\right)$$

Subtract 2 from -4 to get -6.

$$-3x+15=4\left(2x-6\right)$$

Use the distributive property to multiply 4 by 2x-6.

$$-3x+15=8x-24$$

Subtract 8x from both sides.

$$-3x+15-8x=-24$$

Combine -3x and -8x to get -11x.

$$-11x+15=-24$$

Subtract 15 from both sides.

$$-11x=-24-15$$

Subtract 15 from -24 to get -39.

$$-11x=-39$$

Divide both sides by -11.

$$x=\frac{-39}{-11}$$

Fraction \frac{-39}{-11} can be simplified to \frac{39}{11} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{39}{11}$$