Solve 16/-5x-10/3=

$$\frac { 16 } { - 5 } x \frac { - 10 } { 3 } =$$

Evaluate

$$\frac{32x}{3}$$

Solution Steps

Fraction \frac{16}{-5} can be rewritten as -\frac{16}{5} by extracting the negative sign.

$$-\frac{16}{5}x\times \frac{-10}{3}$$

Fraction \frac{-10}{3} can be rewritten as -\frac{10}{3} by extracting the negative sign.

$$-\frac{16}{5}x\left(-\frac{10}{3}\right)$$

Multiply -\frac{16}{5} times -\frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-16\left(-10\right)}{5\times 3}x$$

Do the multiplications in the fraction \frac{-16\left(-10\right)}{5\times 3}.

$$\frac{160}{15}x$$

Reduce the fraction \frac{160}{15} to lowest terms by extracting and canceling out 5.

$$\frac{32}{3}x$$

Differentiate w.r.t. x

$$\frac{32}{3} = 10\frac{2}{3} = 10.666666666666666$$

Steps Using Definition of a Derivative

Fraction \frac{16}{-5} can be rewritten as -\frac{16}{5} by extracting the negative sign.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{16}{5}x\times \frac{-10}{3})$$

Fraction \frac{-10}{3} can be rewritten as -\frac{10}{3} by extracting the negative sign.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{16}{5}x\left(-\frac{10}{3}\right))$$

Multiply -\frac{16}{5} times -\frac{10}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-16\left(-10\right)}{5\times 3}x)$$

Do the multiplications in the fraction \frac{-16\left(-10\right)}{5\times 3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{160}{15}x)$$

Reduce the fraction \frac{160}{15} to lowest terms by extracting and canceling out 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{32}{3}x)$$

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

$$\frac{32}{3}x^{1-1}$$

Subtract 1 from 1.

$$\frac{32}{3}x^{0}$$

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

$$\frac{32}{3}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{32}{3}$$