Solve x-2-3x/2=1+4+5x/3

$$x - \frac { 2 - 3 x } { 2 } = 1 + \frac { 4 + 5 x } { 3 }$$

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.

$$6x-3\left(2-3x\right)=6+2\left(4+5x\right)$$

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

$$6x-6+9x=6+2\left(4+5x\right)$$

Combine 6x and 9x to get 15x.

$$15x-6=6+2\left(4+5x\right)$$

Use the distributive property to multiply 2 by 4+5x.

$$15x-6=6+8+10x$$

Add 6 and 8 to get 14.

$$15x-6=14+10x$$

Subtract 10x from both sides.

$$15x-6-10x=14$$

Combine 15x and -10x to get 5x.

$$5x-6=14$$

Add 6 to both sides.

$$5x=14+6$$

Add 14 and 6 to get 20.

$$5x=20$$

Divide both sides by 5.

$$x=\frac{20}{5}$$

Divide 20 by 5 to get 4.

$$x=4$$