Solve -2x+2/4x+2/4x+x-9/6x=

$$- 2 x + \frac { 2 } { 4 } x + \frac { 2 } { 4 } x + x - \frac { 9 } { 6 } x =$$

Evaluate

$$-\frac{3x}{2}$$

Solution Steps

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$-2x+\frac{1}{2}x+\frac{2}{4}x+x-\frac{9}{6}x$$

Combine -2x and \frac{1}{2}x to get -\frac{3}{2}x.

$$-\frac{3}{2}x+\frac{2}{4}x+x-\frac{9}{6}x$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$-\frac{3}{2}x+\frac{1}{2}x+x-\frac{9}{6}x$$

Combine -\frac{3}{2}x and \frac{1}{2}x to get -x.

$$-x+x-\frac{9}{6}x$$

Combine -x and x to get 0.

$$0-\frac{9}{6}x$$

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

$$0-\frac{3}{2}x$$

Anything plus zero gives itself.

$$-\frac{3}{2}x$$

Differentiate w.r.t. x

$$-\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x+\frac{1}{2}x+\frac{2}{4}x+x-\frac{9}{6}x)$$

Combine -2x and \frac{1}{2}x to get -\frac{3}{2}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{3}{2}x+\frac{2}{4}x+x-\frac{9}{6}x)$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{3}{2}x+\frac{1}{2}x+x-\frac{9}{6}x)$$

Combine -\frac{3}{2}x and \frac{1}{2}x to get -x.

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

Combine -x and x to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(0-\frac{9}{6}x)$$

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(0-\frac{3}{2}x)$$

Anything plus zero gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{3}{2}x)$$

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

$$-\frac{3}{2}x^{1-1}$$

Subtract 1 from 1.

$$-\frac{3}{2}x^{0}$$

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

$$-\frac{3}{2}$$