Solve 2(kx+3)/3-1/2=5(2x+3)/6

$$\frac { 2 ( k x + 3 ) } { 3 } - \frac { 1 } { 2 } = \frac { 5 ( 2 x + 3 ) } { 6 }$$

Solve for k

$$k=\frac{5}{2}+\frac{3}{2x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$2\times 2\left(kx+3\right)-3=5\left(2x+3\right)$$

Multiply 2 and 2 to get 4.

$$4\left(kx+3\right)-3=5\left(2x+3\right)$$

Use the distributive property to multiply 4 by kx+3.

$$4kx+12-3=5\left(2x+3\right)$$

Subtract 3 from 12 to get 9.

$$4kx+9=5\left(2x+3\right)$$

Use the distributive property to multiply 5 by 2x+3.

$$4kx+9=10x+15$$

Subtract 9 from both sides.

$$4kx=10x+15-9$$

Subtract 9 from 15 to get 6.

$$4kx=10x+6$$

The equation is in standard form.

$$4xk=10x+6$$

Divide both sides by 4x.

$$\frac{4xk}{4x}=\frac{10x+6}{4x}$$

Dividing by 4x undoes the multiplication by 4x.

$$k=\frac{10x+6}{4x}$$

Divide 10x+6 by 4x.

$$k=\frac{5}{2}+\frac{3}{2x}$$

Solve for x

$$x=\frac{3}{2k-5}$$

$$k\neq \frac{5}{2}$$

Steps for Solving Linear Equation

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

$$2\times 2\left(kx+3\right)-3=5\left(2x+3\right)$$

Multiply 2 and 2 to get 4.

$$4\left(kx+3\right)-3=5\left(2x+3\right)$$

Use the distributive property to multiply 4 by kx+3.

$$4kx+12-3=5\left(2x+3\right)$$

Subtract 3 from 12 to get 9.

$$4kx+9=5\left(2x+3\right)$$

Use the distributive property to multiply 5 by 2x+3.

$$4kx+9=10x+15$$

Subtract 10x from both sides.

$$4kx+9-10x=15$$

Subtract 9 from both sides.

$$4kx-10x=15-9$$

Subtract 9 from 15 to get 6.

$$4kx-10x=6$$

Combine all terms containing x.

$$\left(4k-10\right)x=6$$

Divide both sides by 4k-10.

$$\frac{\left(4k-10\right)x}{4k-10}=\frac{6}{4k-10}$$

Dividing by 4k-10 undoes the multiplication by 4k-10.

$$x=\frac{6}{4k-10}$$

Divide 6 by 4k-10.

$$x=\frac{3}{2k-5}$$