Trigonometry Examples

$6 - 4 x > x + 2$

Step 1

Move all terms containing $x$ to the left side of the inequality.

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Step 1.1

Subtract $x$ from both sides of the inequality.

$6 - 4 x - x > 2$

Step 1.2

Subtract $x$ from $- 4 x$ .

$6 - 5 x > 2$

Step 2

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

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Step 2.1

Subtract $6$ from both sides of the inequality.

$- 5 x > 2 - 6$

Step 2.2

Subtract $6$ from $2$ .

$- 5 x > - 4$

Step 3

Divide each term in $- 5 x > - 4$ by $- 5$ and simplify.

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Step 3.1

Divide each term in $- 5 x > - 4$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 x}{- 5} < \frac{- 4}{- 5}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 5$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} < \frac{- 4}{- 5}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x < \frac{- 4}{- 5}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Dividing two negative values results in a positive value.

$x < \frac{4}{5}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < \frac{4}{5}$

Interval Notation:

$(- \infty, \frac{4}{5})$