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

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

Solve for x

$$x = \frac{11}{4} = 2\frac{3}{4} = 2.75$$

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 2\left(x-2\right), the least common multiple of 2x-4,2.

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

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

$$2x+5=5x-4+x-2$$

Combine 5x and x to get 6x.

$$2x+5=6x-4-2$$

Subtract 2 from -4 to get -6.

$$2x+5=6x-6$$

Subtract 6x from both sides.

$$2x+5-6x=-6$$

Combine 2x and -6x to get -4x.

$$-4x+5=-6$$

Subtract 5 from both sides.

$$-4x=-6-5$$

Subtract 5 from -6 to get -11.

$$-4x=-11$$

Divide both sides by -4.

$$x=\frac{-11}{-4}$$

Fraction \frac{-11}{-4} can be simplified to \frac{11}{4} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{11}{4}$$