Solve 2x-6/3x-8=2x-5/3x-7

$$\frac { 2 x - 6 } { 3 x - 8 } = \frac { 2 x - 5 } { 3 x - 7 }$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values \frac{7}{3},\frac{8}{3} since division by zero is not defined. Multiply both sides of the equation by \left(3x-8\right)\left(3x-7\right), the least common multiple of 3x-8,3x-7.

$$\left(3x-7\right)\left(2x-6\right)=\left(3x-8\right)\left(2x-5\right)$$

Use the distributive property to multiply 3x-7 by 2x-6 and combine like terms.

$$6x^{2}-32x+42=\left(3x-8\right)\left(2x-5\right)$$

Use the distributive property to multiply 3x-8 by 2x-5 and combine like terms.

$$6x^{2}-32x+42=6x^{2}-31x+40$$

Subtract 6x^{2} from both sides.

$$6x^{2}-32x+42-6x^{2}=-31x+40$$

Combine 6x^{2} and -6x^{2} to get 0.

$$-32x+42=-31x+40$$

Add 31x to both sides.

$$-32x+42+31x=40$$

Combine -32x and 31x to get -x.

$$-x+42=40$$

Subtract 42 from both sides.

$$-x=40-42$$

Subtract 42 from 40 to get -2.

$$-x=-2$$

Multiply both sides by -1.

$$x=2$$