Algebra Examples

$1 - \frac{x^{2}}{6} \leq \frac{\sin (x)}{x} \leq 1$

Step 1

Multiply each term in the inequality by $x$ .

$1 x - \frac{x^{2}}{6} x \leq \frac{\sin (x)}{x} x \leq 1 x$

Step 2

Simplify each term.

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Step 2.1

Multiply $x$ by $1$ .

$x - \frac{x^{2}}{6} \cdot x \leq \frac{\sin (x)}{x} \cdot x \leq 1 x$

Step 2.2

Multiply $- \frac{x^{2}}{6} x$ .

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Step 2.2.1

Combine $x$ and $\frac{x^{2}}{6}$ .

$x - \frac{x \cdot x^{2}}{6} \leq \frac{\sin (x)}{x} \cdot x \leq 1 x$

Step 2.2.2

Multiply $x$ by $x^{2}$ by adding the exponents.

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Step 2.2.2.1

Multiply $x$ by $x^{2}$ .

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Step 2.2.2.1.1

Raise $x$ to the power of $1$ .

$x - \frac{x \cdot x^{2}}{6} \leq \frac{\sin (x)}{x} \cdot x \leq 1 x$

Step 2.2.2.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x - \frac{x^{1 + 2}}{6} \leq \frac{\sin (x)}{x} \cdot x \leq 1 x$

Step 2.2.2.2

Add $1$ and $2$ .

$x - \frac{x^{3}}{6} \leq \frac{\sin (x)}{x} \cdot x \leq 1 x$

Step 3

Cancel the common factor of $x$ .

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Step 3.1

Cancel the common factor.

$x - \frac{x^{3}}{6} \leq \frac{\sin (x)}{x} \cdot x \leq 1 x$

Step 3.2

Rewrite the expression.

$x - \frac{x^{3}}{6} \leq \sin (x) \leq 1 x$

Step 4

Multiply $x$ by $1$ .

$x - \frac{x^{3}}{6} \leq \sin (x) \leq x$

Step 5