Solve x-2/3-x-4/5=x+3/10

$$\frac { x - 2 } { 3 } - \frac { x - 4 } { 5 } = \frac { x + 3 } { 10 }$$

Solve for x

$$x=5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 3,5,10.

$$10\left(x-2\right)-6\left(x-4\right)=3\left(x+3\right)$$

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

$$10x-20-6\left(x-4\right)=3\left(x+3\right)$$

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

$$10x-20-6x+24=3\left(x+3\right)$$

Combine 10x and -6x to get 4x.

$$4x-20+24=3\left(x+3\right)$$

Add -20 and 24 to get 4.

$$4x+4=3\left(x+3\right)$$

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

$$4x+4=3x+9$$

Subtract 3x from both sides.

$$4x+4-3x=9$$

Combine 4x and -3x to get x.

$$x+4=9$$

Subtract 4 from both sides.

$$x=9-4$$

Subtract 4 from 9 to get 5.

$$x=5$$