Solve 1/6-2x-4/5-5x=10/12-4x-3/10-10x

$$\frac { 1 } { 6 - 2 x } - \frac { 4 } { 5 - 5 x } = \frac { 10 } { 12 - 4 x } - \frac { 3 } { 10 - 10 x }$$

Solve for x

$$x = \frac{7}{5} = 1\frac{2}{5} = 1.4$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 1,3 since division by zero is not defined. Multiply both sides of the equation by 20\left(x-3\right)\left(x-1\right), the least common multiple of 6-2x,5-5x,12-4x,10-10x.

$$10-10x-\left(12-4x\right)\times 4=\left(5-5x\right)\times 10-\left(6-2x\right)\times 3$$

Use the distributive property to multiply 12-4x by 4.

$$10-10x-\left(48-16x\right)=\left(5-5x\right)\times 10-\left(6-2x\right)\times 3$$

To find the opposite of 48-16x, find the opposite of each term.

$$10-10x-48+16x=\left(5-5x\right)\times 10-\left(6-2x\right)\times 3$$

Subtract 48 from 10 to get -38.

$$-38-10x+16x=\left(5-5x\right)\times 10-\left(6-2x\right)\times 3$$

Combine -10x and 16x to get 6x.

$$-38+6x=\left(5-5x\right)\times 10-\left(6-2x\right)\times 3$$

Use the distributive property to multiply 5-5x by 10.

$$-38+6x=50-50x-\left(6-2x\right)\times 3$$

Use the distributive property to multiply 6-2x by 3.

$$-38+6x=50-50x-\left(18-6x\right)$$

To find the opposite of 18-6x, find the opposite of each term.

$$-38+6x=50-50x-18+6x$$

Subtract 18 from 50 to get 32.

$$-38+6x=32-50x+6x$$

Combine -50x and 6x to get -44x.

$$-38+6x=32-44x$$

Add 44x to both sides.

$$-38+6x+44x=32$$

Combine 6x and 44x to get 50x.

$$-38+50x=32$$

Add 38 to both sides.

$$50x=32+38$$

Add 32 and 38 to get 70.

$$50x=70$$

Divide both sides by 50.

$$x=\frac{70}{50}$$

Reduce the fraction \frac{70}{50} to lowest terms by extracting and canceling out 10.

$$x=\frac{7}{5}$$