Solve x-3/2+x=2x-13/3+2+x

$$\frac{ x-3 }{ 2 } +x= \frac{ 2x-13 }{ 3 } +2+x$$

Solve for x

$$x=5$$

Steps for Solving Linear Equation

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

$$3\left(x-3\right)+6x=2\left(2x-13\right)+12+6x$$

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

$$3x-9+6x=2\left(2x-13\right)+12+6x$$

Combine 3x and 6x to get 9x.

$$9x-9=2\left(2x-13\right)+12+6x$$

Use the distributive property to multiply 2 by 2x-13.

$$9x-9=4x-26+12+6x$$

Add -26 and 12 to get -14.

$$9x-9=4x-14+6x$$

Combine 4x and 6x to get 10x.

$$9x-9=10x-14$$

Subtract 10x from both sides.

$$9x-9-10x=-14$$

Combine 9x and -10x to get -x.

$$-x-9=-14$$

Add 9 to both sides.

$$-x=-14+9$$

Add -14 and 9 to get -5.

$$-x=-5$$

Multiply both sides by -1.

$$x=5$$