Trigonometry Examples

$4 x + 2 > 14$ $- 21 x + 1 > 22$

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

Subtract $2$ from both sides of the inequality.

$4 x > 14 - 2$

Step 1.1.2

Subtract $2$ from $14$ .

$4 x > 12$

Step 1.2

Divide each term in $4 x > 12$ by $4$ and simplify.

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Step 1.2.1

Divide each term in $4 x > 12$ by $4$ .

$\frac{4 x}{4} > \frac{12}{4}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $4$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} > \frac{12}{4}$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x > \frac{12}{4}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Divide $12$ by $4$ .

$x > 3$

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 $1$ from both sides of the inequality.

$- 21 x > 22 - 1$

Step 2.1.2

Subtract $1$ from $22$ .

$- 21 x > 21$

Step 2.2

Divide each term in $- 21 x > 21$ by $- 21$ and simplify.

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Step 2.2.1

Divide each term in $- 21 x > 21$ by $- 21$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 21 x}{- 21} < \frac{21}{- 21}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $- 21$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{- 21 x}{- 21} < \frac{21}{- 21}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x < \frac{21}{- 21}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $21$ by $- 21$ .

$x < - 1$

Step 3

Plot each graph on the same coordinate system.

$4 x + 2 > 14$

$- 21 x + 1 > 22$

Step 4