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

$$\frac { 2 } { 3 } ( \frac { 3 } { 2 } x + 9 ) - 6$$

Evaluate

$$x$$

Solution Steps

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

$$\frac{2}{3}\times \frac{3}{2}x+\frac{2}{3}\times 9-6$$

Cancel out \frac{2}{3} and its reciprocal \frac{3}{2}.

$$x+\frac{2}{3}\times 9-6$$

Express \frac{2}{3}\times 9 as a single fraction.

$$x+\frac{2\times 9}{3}-6$$

Multiply 2 and 9 to get 18.

$$x+\frac{18}{3}-6$$

Divide 18 by 3 to get 6.

$$x+6-6$$

Subtract 6 from 6 to get 0.

$$x$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{3}\times \frac{3}{2}x+\frac{2}{3}\times 9-6)$$

Cancel out \frac{2}{3} and its reciprocal \frac{3}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x+\frac{2}{3}\times 9-6)$$

Express \frac{2}{3}\times 9 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x+\frac{2\times 9}{3}-6)$$

Multiply 2 and 9 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x+\frac{18}{3}-6)$$

Divide 18 by 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x+6-6)$$

Subtract 6 from 6 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x)$$

The derivative of ax^{n} is nax^{n-1}.

$$x^{1-1}$$

Subtract 1 from 1.

$$x^{0}$$

For any term t except 0, t^{0}=1.

$$1$$