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

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

Solve for x

$$x = \frac{17}{2} = 8\frac{1}{2} = 8.5$$

Steps for Solving Linear Equation

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

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

Multiply 2 and 3 to get 6.

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

Multiply 4 and \frac{1}{4} to get 1.

$$6+2x-3=4\times 5$$

Subtract 3 from 6 to get 3.

$$3+2x=4\times 5$$

Multiply 4 and 5 to get 20.

$$3+2x=20$$

Subtract 3 from both sides.

$$2x=20-3$$

Subtract 3 from 20 to get 17.

$$2x=17$$

Divide both sides by 2.

$$x=\frac{17}{2}$$