Algebra Examples

$- 9 x + 2 > 18$ or $13 x + 15 \leq - 4$

Step 1

Simplify the first inequality.

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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.

$- 9 x > 18 - 2$ or $13 x + 15 \leq - 4$

Step 1.1.2

Subtract $2$ from $18$ .

$- 9 x > 16$ or $13 x + 15 \leq - 4$

Step 1.2

Divide each term in $- 9 x > 16$ by $- 9$ and simplify.

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Step 1.2.1

Divide each term in $- 9 x > 16$ by $- 9$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 9 x}{- 9} < \frac{16}{- 9}$ or $13 x + 15 \leq - 4$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 9$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 9 x}{- 9} < \frac{16}{- 9}$ or $13 x + 15 \leq - 4$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x < \frac{16}{- 9}$ or $13 x + 15 \leq - 4$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Move the negative in front of the fraction.

$x < - \frac{16}{9}$ or $13 x + 15 \leq - 4$

Step 2

Simplify the second inequality.

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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 $15$ from both sides of the inequality.

$x < - \frac{16}{9}$ or $13 x \leq - 4 - 15$

Step 2.1.2

Subtract $15$ from $- 4$ .

$x < - \frac{16}{9}$ or $13 x \leq - 19$

Step 2.2

Divide each term in $13 x \leq - 19$ by $13$ and simplify.

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Step 2.2.1

Divide each term in $13 x \leq - 19$ by $13$ .

$x < - \frac{16}{9}$ or $\frac{13 x}{13} \leq \frac{- 19}{13}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $13$ .

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Step 2.2.2.1.1

Cancel the common factor.

$x < - \frac{16}{9}$ or $\frac{13 x}{13} \leq \frac{- 19}{13}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x < - \frac{16}{9}$ or $x \leq \frac{- 19}{13}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Move the negative in front of the fraction.

$x < - \frac{16}{9}$ or $x \leq - \frac{19}{13}$

Step 3

The union consists of all of the elements that are contained in each interval.

$x \leq - \frac{19}{13}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq - \frac{19}{13}$

Interval Notation:

$(- \infty, - \frac{19}{13}]$

Step 5