Precalculus Examples

$11 x + 12 < 22 x - 4$

Step 1

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

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Step 1.1

Subtract $22 x$ from both sides of the inequality.

$11 x + 12 - 22 x < - 4$

Step 1.2

Subtract $22 x$ from $11 x$ .

$- 11 x + 12 < - 4$

Step 2

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

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Step 2.1

Subtract $12$ from both sides of the inequality.

$- 11 x < - 4 - 12$

Step 2.2

Subtract $12$ from $- 4$ .

$- 11 x < - 16$

Step 3

Divide each term in $- 11 x < - 16$ by $- 11$ and simplify.

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Step 3.1

Divide each term in $- 11 x < - 16$ by $- 11$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 11 x}{- 11} > \frac{- 16}{- 11}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 11$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 11 x}{- 11} > \frac{- 16}{- 11}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x > \frac{- 16}{- 11}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Dividing two negative values results in a positive value.

$x > \frac{16}{11}$

Step 4

Convert the inequality to interval notation.

$(\frac{16}{11}, \infty)$

Step 5