Solve 2x-5/3x-6=5x-4/2x-4+1/2

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

Solve for x

$$x=\frac{4}{7}\approx 0.571428571$$

Steps for Solving Linear Equation

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

$$2\left(2x-5\right)=3\left(5x-4\right)+6\left(x-2\right)\times \frac{1}{2}$$

Use the distributive property to multiply 2 by 2x-5.

$$4x-10=3\left(5x-4\right)+6\left(x-2\right)\times \frac{1}{2}$$

Use the distributive property to multiply 3 by 5x-4.

$$4x-10=15x-12+6\left(x-2\right)\times \frac{1}{2}$$

Multiply 6 and \frac{1}{2} to get 3.

$$4x-10=15x-12+3\left(x-2\right)$$

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

$$4x-10=15x-12+3x-6$$

Combine 15x and 3x to get 18x.

$$4x-10=18x-12-6$$

Subtract 6 from -12 to get -18.

$$4x-10=18x-18$$

Subtract 18x from both sides.

$$4x-10-18x=-18$$

Combine 4x and -18x to get -14x.

$$-14x-10=-18$$

Add 10 to both sides.

$$-14x=-18+10$$

Add -18 and 10 to get -8.

$$-14x=-8$$

Divide both sides by -14.

$$x=\frac{-8}{-14}$$

Reduce the fraction \frac{-8}{-14} to lowest terms by extracting and canceling out -2.

$$x=\frac{4}{7}$$