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

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

Solve for x

$$x=-\frac{2}{7}\approx -0.285714286$$

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 2x, the least common multiple of 2x,2.

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

Multiply 2 and -4 to get -8.

$$1-8x+2x\times \frac{1}{2}=3$$

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

$$1-8x+x=3$$

Combine -8x and x to get -7x.

$$1-7x=3$$

Subtract 1 from both sides.

$$-7x=3-1$$

Subtract 1 from 3 to get 2.

$$-7x=2$$

Divide both sides by -7.

$$x=\frac{2}{-7}$$

Fraction \frac{2}{-7} can be rewritten as -\frac{2}{7} by extracting the negative sign.

$$x=-\frac{2}{7}$$