Algebra Examples

$- 13 > - x - 9$ or $- x - 9 \leq - 21$

Step 1

Simplify the first inequality.

Tap for more steps...

Step 1.1

Rewrite so $x$ is on the left side of the inequality.

$- x - 9 < - 13$ or $- x - 9 \leq - 21$

Step 1.2

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

Tap for more steps...

Step 1.2.1

Add $9$ to both sides of the inequality.

$- x < - 13 + 9$ or $- x - 9 \leq - 21$

Step 1.2.2

Add $- 13$ and $9$ .

$- x < - 4$ or $- x - 9 \leq - 21$

Step 1.3

Divide each term in $- x < - 4$ by $- 1$ and simplify.

Tap for more steps...

Step 1.3.1

Divide each term in $- x < - 4$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} > \frac{- 4}{- 1}$ or $- x - 9 \leq - 21$

Step 1.3.2

Simplify the left side.

Tap for more steps...

Step 1.3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} > \frac{- 4}{- 1}$ or $- x - 9 \leq - 21$

Step 1.3.2.2

Divide $x$ by $1$ .

$x > \frac{- 4}{- 1}$ or $- x - 9 \leq - 21$

Step 1.3.3

Simplify the right side.

Tap for more steps...

Step 1.3.3.1

Divide $- 4$ by $- 1$ .

$x > 4$ or $- x - 9 \leq - 21$

Step 2

Simplify the second inequality.

Tap for more steps...

Step 2.1

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

Tap for more steps...

Step 2.1.1

Add $9$ to both sides of the inequality.

$x > 4$ or $- x \leq - 21 + 9$

Step 2.1.2

Add $- 21$ and $9$ .

$x > 4$ or $- x \leq - 12$

Step 2.2

Divide each term in $- x \leq - 12$ by $- 1$ and simplify.

Tap for more steps...

Step 2.2.1

Divide each term in $- x \leq - 12$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$x > 4$ or $\frac{- x}{- 1} \geq \frac{- 12}{- 1}$

Step 2.2.2

Simplify the left side.

Tap for more steps...

Step 2.2.2.1

Dividing two negative values results in a positive value.

$x > 4$ or $\frac{x}{1} \geq \frac{- 12}{- 1}$

Step 2.2.2.2

Divide $x$ by $1$ .

$x > 4$ or $x \geq \frac{- 12}{- 1}$

Step 2.2.3

Simplify the right side.

Tap for more steps...

Step 2.2.3.1

Divide $- 12$ by $- 1$ .

$x > 4$ or $x \geq 12$

Step 3

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

$x > 4$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > 4$

Interval Notation:

$(4, \infty)$

Step 5