Solve 1/6-2x-4/5-5x=10/12-4x-13/10-10x

$$\frac { 1 } { 6 - 2 x } - \frac { 4 } { 5 - 5 x } = \frac { 10 } { 12 - 4 x } - \frac { 13 } { 10 - 10 x }$$

Solve for x

$$x=\frac{1}{3}\approx 0.333333333$$

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.

$$10-10x-\left(12-4x\right)\times 4=\left(5-5x\right)\times 10-\left(6-2x\right)\times 13$$

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

$$10-10x-\left(48-16x\right)=\left(5-5x\right)\times 10-\left(6-2x\right)\times 13$$

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

$$10-10x-48+16x=\left(5-5x\right)\times 10-\left(6-2x\right)\times 13$$

Subtract 48 from 10 to get -38.

$$-38-10x+16x=\left(5-5x\right)\times 10-\left(6-2x\right)\times 13$$

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

$$-38+6x=\left(5-5x\right)\times 10-\left(6-2x\right)\times 13$$

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

$$-38+6x=50-50x-\left(6-2x\right)\times 13$$

Use the distributive property to multiply 6-2x by 13.

$$-38+6x=50-50x-\left(78-26x\right)$$

To find the opposite of 78-26x, find the opposite of each term.

$$-38+6x=50-50x-78+26x$$

Subtract 78 from 50 to get -28.

$$-38+6x=-28-50x+26x$$

Combine -50x and 26x to get -24x.

$$-38+6x=-28-24x$$

Add 24x to both sides.

$$-38+6x+24x=-28$$

Combine 6x and 24x to get 30x.

$$-38+30x=-28$$

Add 38 to both sides.

$$30x=-28+38$$

Add -28 and 38 to get 10.

$$30x=10$$

Divide both sides by 30.

$$x=\frac{10}{30}$$

Reduce the fraction \frac{10}{30} to lowest terms by extracting and canceling out 10.

$$x=\frac{1}{3}$$