How to solve (3)/(8)x(16)/(27)

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve (3)/(8)x(16)/(27) | Equatix

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Question

$$\frac{ 3 }{ 8 } x \frac{ 16 }{ 27 }$$

Evaluate

$\frac{2x}{9}$

Solution Steps

Multiply $\frac{3}{8}$ times $\frac{16}{27}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 16}{8\times 27}x$$

Do the multiplications in the fraction $\frac{3\times 16}{8\times 27}$.

$$\frac{48}{216}x$$

Reduce the fraction $\frac{48}{216}$ to lowest terms by extracting and canceling out $24$.

$$\frac{2}{9}x$$

Show Solution

Differentiate w.r.t. x

$\frac{2}{9} = 0.2222222222222222$

Steps Using Definition of a Derivative

Multiply $\frac{3}{8}$ times $\frac{16}{27}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\times 16}{8\times 27}x)$$

Do the multiplications in the fraction $\frac{3\times 16}{8\times 27}$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{48}{216}x)$$

Reduce the fraction $\frac{48}{216}$ to lowest terms by extracting and canceling out $24$.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{9}x)$$

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

$$\frac{2}{9}x^{1-1}$$

Subtract $1$ from $1$.

$$\frac{2}{9}x^{0}$$

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

$$\frac{2}{9}\times 1$$

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

$$\frac{2}{9}$$