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

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

Solve for x

$$x = \frac{67}{8} = 8\frac{3}{8} = 8.375$$

Steps for Solving Linear Equation

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

$$6\times 3\left(x+1\right)-6\left(3x-4\right)=4\times 2\left(x-2\right)-9$$

Multiply 6 and 3 to get 18.

$$18\left(x+1\right)-6\left(3x-4\right)=4\times 2\left(x-2\right)-9$$

Use the distributive property to multiply 18 by x+1.

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

Use the distributive property to multiply -6 by 3x-4.

$$18x+18-18x+24=4\times 2\left(x-2\right)-9$$

Combine 18x and -18x to get 0.

$$18+24=4\times 2\left(x-2\right)-9$$

Add 18 and 24 to get 42.

$$42=4\times 2\left(x-2\right)-9$$

Multiply 4 and 2 to get 8.

$$42=8\left(x-2\right)-9$$

Use the distributive property to multiply 8 by x-2.

$$42=8x-16-9$$

Subtract 9 from -16 to get -25.

$$42=8x-25$$

Swap sides so that all variable terms are on the left hand side.

$$8x-25=42$$

Add 25 to both sides.

$$8x=42+25$$

Add 42 and 25 to get 67.

$$8x=67$$

Divide both sides by 8.

$$x=\frac{67}{8}$$