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

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

Solve for x

$$x = \frac{25}{7} = 3\frac{4}{7} \approx 3.571428571$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 5,2,3.

$$6\times 3x-15\left(x-3\right)=10\left(x+2\right)$$

Multiply 6 and 3 to get 18.

$$18x-15\left(x-3\right)=10\left(x+2\right)$$

Use the distributive property to multiply -15 by x-3.

$$18x-15x+45=10\left(x+2\right)$$

Combine 18x and -15x to get 3x.

$$3x+45=10\left(x+2\right)$$

Use the distributive property to multiply 10 by x+2.

$$3x+45=10x+20$$

Subtract 10x from both sides.

$$3x+45-10x=20$$

Combine 3x and -10x to get -7x.

$$-7x+45=20$$

Subtract 45 from both sides.

$$-7x=20-45$$

Subtract 45 from 20 to get -25.

$$-7x=-25$$

Divide both sides by -7.

$$x=\frac{-25}{-7}$$

Fraction \frac{-25}{-7} can be simplified to \frac{25}{7} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{25}{7}$$