Solve x-1/5-x-2/8=x-1/4-x-2/10-frac{1}{20}

$$\frac{ x-1 }{ 5 } - \frac{ x-2 }{ 8 } = \frac{ x-1 }{ 4 } - \frac{ x-2 }{ 10 } - \frac{ 1 }{ 20 }$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 40, the least common multiple of 5,8,4,10,20.

$$8\left(x-1\right)-5\left(x-2\right)=10\left(x-1\right)-4\left(x-2\right)-2$$

Use the distributive property to multiply 8 by x-1.

$$8x-8-5\left(x-2\right)=10\left(x-1\right)-4\left(x-2\right)-2$$

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

$$8x-8-5x+10=10\left(x-1\right)-4\left(x-2\right)-2$$

Combine 8x and -5x to get 3x.

$$3x-8+10=10\left(x-1\right)-4\left(x-2\right)-2$$

Add -8 and 10 to get 2.

$$3x+2=10\left(x-1\right)-4\left(x-2\right)-2$$

Use the distributive property to multiply 10 by x-1.

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

Use the distributive property to multiply -4 by x-2.

$$3x+2=10x-10-4x+8-2$$

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

$$3x+2=6x-10+8-2$$

Add -10 and 8 to get -2.

$$3x+2=6x-2-2$$

Subtract 2 from -2 to get -4.

$$3x+2=6x-4$$

Subtract 6x from both sides.

$$3x+2-6x=-4$$

Combine 3x and -6x to get -3x.

$$-3x+2=-4$$

Subtract 2 from both sides.

$$-3x=-4-2$$

Subtract 2 from -4 to get -6.

$$-3x=-6$$

Divide both sides by -3.

$$x=\frac{-6}{-3}$$

Divide -6 by -3 to get 2.

$$x=2$$