Solve x-1/2x-1/2=2x-4/3x^2

$$\frac { x - 1 } { 2 x } - \frac { 1 } { 2 } = \frac { 2 x - 4 } { 3 x ^ { 2 } }$$

Solve for x

$$x = \frac{8}{7} = 1\frac{1}{7} \approx 1.142857143$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 6x^{2}, the least common multiple of 2x,2,3x^{2}.

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

Use the distributive property to multiply 3x by x-1.

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

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

$$3x^{2}-3x-3x^{2}=2\left(2x-4\right)$$

Combine 3x^{2} and -3x^{2} to get 0.

$$-3x=2\left(2x-4\right)$$

Use the distributive property to multiply 2 by 2x-4.

$$-3x=4x-8$$

Subtract 4x from both sides.

$$-3x-4x=-8$$

Combine -3x and -4x to get -7x.

$$-7x=-8$$

Divide both sides by -7.

$$x=\frac{-8}{-7}$$

Fraction \frac{-8}{-7} can be simplified to \frac{8}{7} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{8}{7}$$