Solve 2kx+3/3=k-2+x/2

$$\frac { 2 k x + 3 } { 3 } = \frac { k - 2 + x } { 2 }$$

Solve for k

$$k=-\frac{3\left(4-x\right)}{4x-3}$$

$$x\neq \frac{3}{4}$$

Steps for Solving Linear Equation

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

$$2\left(2kx+3\right)=3\left(k-2+x\right)$$

Use the distributive property to multiply 2 by 2kx+3.

$$4kx+6=3\left(k-2+x\right)$$

Use the distributive property to multiply 3 by k-2+x.

$$4kx+6=3k-6+3x$$

Subtract 3k from both sides.

$$4kx+6-3k=-6+3x$$

Subtract 6 from both sides.

$$4kx-3k=-6+3x-6$$

Subtract 6 from -6 to get -12.

$$4kx-3k=-12+3x$$

Combine all terms containing k.

$$\left(4x-3\right)k=-12+3x$$

The equation is in standard form.

$$\left(4x-3\right)k=3x-12$$

Divide both sides by 4x-3.

$$\frac{\left(4x-3\right)k}{4x-3}=\frac{3x-12}{4x-3}$$

Dividing by 4x-3 undoes the multiplication by 4x-3.

$$k=\frac{3x-12}{4x-3}$$

Divide -12+3x by 4x-3.

$$k=\frac{3\left(x-4\right)}{4x-3}$$

Solve for x

$$x=-\frac{3\left(4-k\right)}{4k-3}$$

$$k\neq \frac{3}{4}$$

Steps for Solving Linear Equation

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

$$2\left(2kx+3\right)=3\left(k-2+x\right)$$

Use the distributive property to multiply 2 by 2kx+3.

$$4xk+6=3\left(k-2+x\right)$$

Use the distributive property to multiply 3 by k-2+x.

$$4xk+6=3k-6+3x$$

Subtract 3x from both sides.

$$4xk+6-3x=3k-6$$

Subtract 6 from both sides.

$$4xk-3x=3k-6-6$$

Subtract 6 from -6 to get -12.

$$4xk-3x=3k-12$$

Combine all terms containing x.

$$\left(4k-3\right)x=3k-12$$

Divide both sides by 4k-3.

$$\frac{\left(4k-3\right)x}{4k-3}=\frac{3k-12}{4k-3}$$

Dividing by 4k-3 undoes the multiplication by 4k-3.

$$x=\frac{3k-12}{4k-3}$$

Divide -12+3k by 4k-3.

$$x=\frac{3\left(k-4\right)}{4k-3}$$