Algebra Examples

$- 2 m - 14 \leq - 22$ and $3 m + 14 \geq 8$

Step 1

Simplify the first inequality.

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

Add $14$ to both sides of the inequality.

$- 2 m \leq - 22 + 14$

Step 1.1.2

Add $- 22$ and $14$ .

$- 2 m \leq - 8$

Step 1.2

Divide each term in $- 2 m \leq - 8$ by $- 2$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in $- 2 m \leq - 8$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 m}{- 2} \geq \frac{- 8}{- 2}$

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.

$\frac{- 2 m}{- 2} \geq \frac{- 8}{- 2}$

Step 1.2.2.1.2

Divide $m$ by $1$ .

$m \geq \frac{- 8}{- 2}$

Step 1.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.3.1

Divide $- 8$ by $- 2$ .

$m \geq 4$

Step 2

Simplify the second inequality.

Tap for more steps...

Step 2.1

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

Tap for more steps...

Step 2.1.1

Subtract $14$ from both sides of the inequality.

$3 m \geq 8 - 14$

Step 2.1.2

Subtract $14$ from $8$ .

$3 m \geq - 6$

Step 2.2

Divide each term in $3 m \geq - 6$ by $3$ and simplify.

Tap for more steps...

Step 2.2.1

Divide each term in $3 m \geq - 6$ by $3$ .

$\frac{3 m}{3} \geq \frac{- 6}{3}$

Step 2.2.2

Simplify the left side.

Tap for more steps...

Step 2.2.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.2.2.1.1

Cancel the common factor.

$\frac{3 m}{3} \geq \frac{- 6}{3}$

Step 2.2.2.1.2

Divide $m$ by $1$ .

$m \geq \frac{- 6}{3}$

Step 2.2.3

Simplify the right side.

Tap for more steps...

Step 2.2.3.1

Divide $- 6$ by $3$ .

$m \geq - 2$

Step 3

The intersection consists of the elements that are contained in both intervals.

$m \geq 4$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$m \geq 4$

Interval Notation:

$[4, \infty)$

Step 5