Solve x-2/3+2=x-2/5+6

$$\frac { x - 2 } { 3 } + 2 = \frac { x - 2 } { 5 } + 6$$

Solve for x

$$x=32$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 3,5.

$$5\left(x-2\right)+30=3\left(x-2\right)+90$$

Use the distributive property to multiply 5 by x-2.

$$5x-10+30=3\left(x-2\right)+90$$

Add -10 and 30 to get 20.

$$5x+20=3\left(x-2\right)+90$$

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

$$5x+20=3x-6+90$$

Add -6 and 90 to get 84.

$$5x+20=3x+84$$

Subtract 3x from both sides.

$$5x+20-3x=84$$

Combine 5x and -3x to get 2x.

$$2x+20=84$$

Subtract 20 from both sides.

$$2x=84-20$$

Subtract 20 from 84 to get 64.

$$2x=64$$

Divide both sides by 2.

$$x=\frac{64}{2}$$

Divide 64 by 2 to get 32.

$$x=32$$