Solve 2/3(1/3x-1/2)=4x+21/2i

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

Solve for x

$$x=-\frac{3}{34}-\frac{45}{68}i\approx -0.088235294-0.661764706i$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$4\left(\frac{1}{3}x-\frac{1}{2}\right)=24x+3\left(2\times 2+1\right)i$$

Use the distributive property to multiply 4 by \frac{1}{3}x-\frac{1}{2}.

$$4\times \frac{1}{3}x+4\left(-\frac{1}{2}\right)=24x+3\left(2\times 2+1\right)i$$

Multiply 4 and \frac{1}{3} to get \frac{4}{3}.

$$\frac{4}{3}x+4\left(-\frac{1}{2}\right)=24x+3\left(2\times 2+1\right)i$$

Express 4\left(-\frac{1}{2}\right) as a single fraction.

$$\frac{4}{3}x+\frac{4\left(-1\right)}{2}=24x+3\left(2\times 2+1\right)i$$

Multiply 4 and -1 to get -4.

$$\frac{4}{3}x+\frac{-4}{2}=24x+3\left(2\times 2+1\right)i$$

Divide -4 by 2 to get -2.

$$\frac{4}{3}x-2=24x+3\left(2\times 2+1\right)i$$

Multiply 2 and 2 to get 4.

$$\frac{4}{3}x-2=24x+3\left(4+1\right)i$$

Add 4 and 1 to get 5.

$$\frac{4}{3}x-2=24x+3\times \left(5i\right)$$

Multiply 3 and 5i to get 15i.

$$\frac{4}{3}x-2=24x+15i$$

Subtract 24x from both sides.

$$\frac{4}{3}x-2-24x=15i$$

Combine \frac{4}{3}x and -24x to get -\frac{68}{3}x.

$$-\frac{68}{3}x-2=15i$$

Add 2 to both sides.

$$-\frac{68}{3}x=15i+2$$

The equation is in standard form.

$$-\frac{68}{3}x=2+15i$$

Divide both sides of the equation by -\frac{68}{3}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{68}{3}x}{-\frac{68}{3}}=\frac{2+15i}{-\frac{68}{3}}$$

Dividing by -\frac{68}{3} undoes the multiplication by -\frac{68}{3}.

$$x=\frac{2+15i}{-\frac{68}{3}}$$

Divide 2+15i by -\frac{68}{3} by multiplying 2+15i by the reciprocal of -\frac{68}{3}.

$$x=-\frac{3}{34}-\frac{45}{68}i$$