Solve 2/3x-4-1/20=5/6x-8

$$\frac { 2 } { 3 x - 4 } - \frac { 1 } { 20 } = \frac { 5 } { 6 x - 8 }$$

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

Variable x cannot be equal to \frac{4}{3} since division by zero is not defined. Multiply both sides of the equation by 20\left(3x-4\right), the least common multiple of 3x-4,20,6x-8.

$$20\times 2+20\left(3x-4\right)\left(-\frac{1}{20}\right)=10\times 5$$

Multiply 20 and 2 to get 40.

$$40+20\left(3x-4\right)\left(-\frac{1}{20}\right)=10\times 5$$

Multiply 20 and -\frac{1}{20} to get -1.

$$40-\left(3x-4\right)=10\times 5$$

To find the opposite of 3x-4, find the opposite of each term.

$$40-3x+4=10\times 5$$

Add 40 and 4 to get 44.

$$44-3x=10\times 5$$

Multiply 10 and 5 to get 50.

$$44-3x=50$$

Subtract 44 from both sides.

$$-3x=50-44$$

Subtract 44 from 50 to get 6.

$$-3x=6$$

Divide both sides by -3.

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

Divide 6 by -3 to get -2.

$$x=-2$$