Trigonometry Examples

$a b < a d$

Step 1

Subtract $a d$ from both sides of the inequality.

$a b - a d < 0$

Step 2

Factor $a$ out of $a b - a d$ .

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Step 2.1

Factor $a$ out of $a b$ .

$a (b) - a d < 0$

Step 2.2

Factor $a$ out of $- a d$ .

$a (b) + a (- 1 d) < 0$

Step 2.3

Factor $a$ out of $a (b) + a (- 1 d)$ .

$a (b - 1 d) < 0$

$a (b - 1 d) < 0$

Step 3

Rewrite $- 1 d$ as $- d$ .

$a (b - d) < 0$

Step 4

Divide each term in $a (b - d) < 0$ by $b - d$ and simplify.

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Step 4.1

Divide each term in $a (b - d) < 0$ by $b - d$ .

$\frac{a (b - d)}{b - d} < \frac{0}{b - d}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $b - d$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{a (b - d)}{b - d} < \frac{0}{b - d}$

Step 4.2.1.2

Divide $a$ by $1$ .

$a < \frac{0}{b - d}$

$a < \frac{0}{b - d}$

$a < \frac{0}{b - d}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $b - d$ .

$a < 0$

$a < 0$

$a < 0$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$a < 0$

Interval Notation:

$(- \infty, 0)$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$