Trigonometry Examples

$7 x + 1 < 2 x - 4$

Step 1

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

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Step 1.1

Subtract $2 x$ from both sides of the inequality.

$7 x + 1 - 2 x < - 4$

Step 1.2

Subtract $2 x$ from $7 x$ .

$5 x + 1 < - 4$

Step 2

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

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Step 2.1

Subtract $1$ from both sides of the inequality.

$5 x < - 4 - 1$

Step 2.2

Subtract $1$ from $- 4$ .

$5 x < - 5$

Step 3

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

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Step 3.1

Divide each term in $5 x < - 5$ by $5$ .

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

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.

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

Step 3.2.1.2

Divide $x$ by $1$ .

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

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $- 5$ by $5$ .

$x < - 1$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < - 1$

Interval Notation:

$(- \infty, - 1)$