Solve x-2/8-x-3/2-x-2/4=-x+4/5

$$\frac { x - 2 } { 8 } - \frac { x - 3 } { 2 } - \frac { x - 2 } { 4 } = - \frac { x + 4 } { 5 }$$

Solve for x

$$x=6$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 40, the least common multiple of 8,2,4,5.

$$5\left(x-2\right)-20\left(x-3\right)-10\left(x-2\right)=-8\left(x+4\right)$$

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

$$5x-10-20\left(x-3\right)-10\left(x-2\right)=-8\left(x+4\right)$$

Use the distributive property to multiply -20 by x-3.

$$5x-10-20x+60-10\left(x-2\right)=-8\left(x+4\right)$$

Combine 5x and -20x to get -15x.

$$-15x-10+60-10\left(x-2\right)=-8\left(x+4\right)$$

Add -10 and 60 to get 50.

$$-15x+50-10\left(x-2\right)=-8\left(x+4\right)$$

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

$$-15x+50-10x+20=-8\left(x+4\right)$$

Combine -15x and -10x to get -25x.

$$-25x+50+20=-8\left(x+4\right)$$

Add 50 and 20 to get 70.

$$-25x+70=-8\left(x+4\right)$$

Use the distributive property to multiply -8 by x+4.

$$-25x+70=-8x-32$$

Add 8x to both sides.

$$-25x+70+8x=-32$$

Combine -25x and 8x to get -17x.

$$-17x+70=-32$$

Subtract 70 from both sides.

$$-17x=-32-70$$

Subtract 70 from -32 to get -102.

$$-17x=-102$$

Divide both sides by -17.

$$x=\frac{-102}{-17}$$

Divide -102 by -17 to get 6.

$$x=6$$