Solve 9x+6(-3/2x-9/2)=-27

$$9 x + 6 ( - 3 / 2 x - 9 / 2 ) = - 27$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

Solution Steps

Use the distributive property to multiply 6 by -\frac{3}{2}x-\frac{9}{2}.

$$9x+6\left(-\frac{3}{2}\right)x+6\left(-\frac{9}{2}\right)=-27$$

Express 6\left(-\frac{3}{2}\right) as a single fraction.

$$9x+\frac{6\left(-3\right)}{2}x+6\left(-\frac{9}{2}\right)=-27$$

Multiply 6 and -3 to get -18.

$$9x+\frac{-18}{2}x+6\left(-\frac{9}{2}\right)=-27$$

Divide -18 by 2 to get -9.

$$9x-9x+6\left(-\frac{9}{2}\right)=-27$$

Express 6\left(-\frac{9}{2}\right) as a single fraction.

$$9x-9x+\frac{6\left(-9\right)}{2}=-27$$

Multiply 6 and -9 to get -54.

$$9x-9x+\frac{-54}{2}=-27$$

Divide -54 by 2 to get -27.

$$9x-9x-27=-27$$

Combine 9x and -9x to get 0.

$$-27=-27$$

Compare -27 and -27.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{C}$$

Solve for x

$$x\in \mathrm{R}$$

Solution Steps

Use the distributive property to multiply 6 by -\frac{3}{2}x-\frac{9}{2}.

$$9x+6\left(-\frac{3}{2}\right)x+6\left(-\frac{9}{2}\right)=-27$$

Express 6\left(-\frac{3}{2}\right) as a single fraction.

$$9x+\frac{6\left(-3\right)}{2}x+6\left(-\frac{9}{2}\right)=-27$$

Multiply 6 and -3 to get -18.

$$9x+\frac{-18}{2}x+6\left(-\frac{9}{2}\right)=-27$$

Divide -18 by 2 to get -9.

$$9x-9x+6\left(-\frac{9}{2}\right)=-27$$

Express 6\left(-\frac{9}{2}\right) as a single fraction.

$$9x-9x+\frac{6\left(-9\right)}{2}=-27$$

Multiply 6 and -9 to get -54.

$$9x-9x+\frac{-54}{2}=-27$$

Divide -54 by 2 to get -27.

$$9x-9x-27=-27$$

Combine 9x and -9x to get 0.

$$-27=-27$$

Compare -27 and -27.

$$\text{true}$$

This is true for any x.

$$x\in \mathrm{R}$$