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

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

Solve for x

$$x=-4$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply 3 by 2x-3.

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

Use the distributive property to multiply 2 by x+1.

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

Combine 6x and 2x to get 8x.

$$8x-9+2=3\left(3x-1\right)$$

Add -9 and 2 to get -7.

$$8x-7=3\left(3x-1\right)$$

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

$$8x-7=9x-3$$

Subtract 9x from both sides.

$$8x-7-9x=-3$$

Combine 8x and -9x to get -x.

$$-x-7=-3$$

Add 7 to both sides.

$$-x=-3+7$$

Add -3 and 7 to get 4.

$$-x=4$$

Multiply both sides by -1.

$$x=-4$$