Trigonometry Examples

$6 x - 21 \geq - 3$ $14 x + 11 < - 17$

Step 1

Solve for $x$ .

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Step 1.1

Move all terms not containing $x$ to the right side of the inequality.

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Step 1.1.1

Add $21$ to both sides of the inequality.

$6 x \geq - 3 + 21$

Step 1.1.2

Add $- 3$ and $21$ .

$6 x \geq 18$

Step 1.2

Divide each term in $6 x \geq 18$ by $6$ and simplify.

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Step 1.2.1

Divide each term in $6 x \geq 18$ by $6$ .

$\frac{6 x}{6} \geq \frac{18}{6}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $6$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{6 x}{6} \geq \frac{18}{6}$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{18}{6}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Divide $18$ by $6$ .

$x \geq 3$

Step 2

Solve for $x$ .

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Step 2.1

Move all terms not containing $x$ to the right side of the inequality.

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Step 2.1.1

Subtract $11$ from both sides of the inequality.

$14 x < - 17 - 11$

Step 2.1.2

Subtract $11$ from $- 17$ .

$14 x < - 28$

Step 2.2

Divide each term in $14 x < - 28$ by $14$ and simplify.

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Step 2.2.1

Divide each term in $14 x < - 28$ by $14$ .

$\frac{14 x}{14} < \frac{- 28}{14}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $14$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{14 x}{14} < \frac{- 28}{14}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x < \frac{- 28}{14}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $- 28$ by $14$ .

$x < - 2$

Step 3

Plot each graph on the same coordinate system.

$6 x - 21 \geq - 3$

$14 x + 11 < - 17$

Step 4