Solve 6/19=x-12/2x-2

$$\frac { 6 } { 19 } = \frac { x - 12 } { 2 x - 2 }$$

Solve for x

$$x = \frac{216}{7} = 30\frac{6}{7} \approx 30.857142857$$

Steps for Solving Linear Equation

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by 38\left(x-1\right), the least common multiple of 19,2x-2.

$$12\left(x-1\right)=19\left(x-12\right)$$

Use the distributive property to multiply 12 by x-1.

$$12x-12=19\left(x-12\right)$$

Use the distributive property to multiply 19 by x-12.

$$12x-12=19x-228$$

Subtract 19x from both sides.

$$12x-12-19x=-228$$

Combine 12x and -19x to get -7x.

$$-7x-12=-228$$

Add 12 to both sides.

$$-7x=-228+12$$

Add -228 and 12 to get -216.

$$-7x=-216$$

Divide both sides by -7.

$$x=\frac{-216}{-7}$$

Fraction \frac{-216}{-7} can be simplified to \frac{216}{7} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{216}{7}$$