Algebra Examples

$- 2 x + 6 \geq 0$ or $- 10 < - 2 x + 6$

Step 1

Simplify the first inequality.

Tap for more steps...

Step 1.1

Subtract $6$ from both sides of the inequality.

$- 2 x \geq - 6$ or $- 10 < - 2 x + 6$

Step 1.2

Divide each term in $- 2 x \geq - 6$ by $- 2$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in $- 2 x \geq - 6$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} \leq \frac{- 6}{- 2}$ or $- 10 < - 2 x + 6$

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Cancel the common factor of $- 2$ .

Tap for more steps...

Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} \leq \frac{- 6}{- 2}$ or $- 10 < - 2 x + 6$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x \leq \frac{- 6}{- 2}$ or $- 10 < - 2 x + 6$

Step 1.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.3.1

Divide $- 6$ by $- 2$ .

$x \leq 3$ or $- 10 < - 2 x + 6$

Step 2

Simplify the second inequality.

Tap for more steps...

Step 2.1

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

$x \leq 3$ or $- 2 x + 6 > - 10$

Step 2.2

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

Tap for more steps...

Step 2.2.1

Subtract $6$ from both sides of the inequality.

$x \leq 3$ or $- 2 x > - 10 - 6$

Step 2.2.2

Subtract $6$ from $- 10$ .

$x \leq 3$ or $- 2 x > - 16$

Step 2.3

Divide each term in $- 2 x > - 16$ by $- 2$ and simplify.

Tap for more steps...

Step 2.3.1

Divide each term in $- 2 x > - 16$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$x \leq 3$ or $\frac{- 2 x}{- 2} < \frac{- 16}{- 2}$

Step 2.3.2

Simplify the left side.

Tap for more steps...

Step 2.3.2.1

Cancel the common factor of $- 2$ .

Tap for more steps...

Step 2.3.2.1.1

Cancel the common factor.

$x \leq 3$ or $\frac{- 2 x}{- 2} < \frac{- 16}{- 2}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x \leq 3$ or $x < \frac{- 16}{- 2}$

Step 2.3.3

Simplify the right side.

Tap for more steps...

Step 2.3.3.1

Divide $- 16$ by $- 2$ .

$x \leq 3$ or $x < 8$

Step 3

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

$x < 8$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < 8$

Interval Notation:

$(- \infty, 8)$

Step 5