Solve the System of Inequalities 12+4n>44 or 10-12n>-38

$12 + 4 n > 44$ or $10 - 12 n > - 38$

Step 1

Simplify the first inequality.

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

Subtract $12$ from both sides of the inequality.

$4 n > 44 - 12$ or $10 - 12 n > - 38$

Subtract $12$ from $44$ .

$4 n > 32$ or $10 - 12 n > - 38$

Divide each term in $4 n > 32$ by $4$ and simplify.

Divide each term in $4 n > 32$ by $4$ .

$\frac{4 n}{4} > \frac{32}{4}$ or $10 - 12 n > - 38$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 n}{4} > \frac{32}{4}$ or $10 - 12 n > - 38$

Divide $n$ by $1$ .

$n > \frac{32}{4}$ or $10 - 12 n > - 38$

Simplify the right side.

Divide $32$ by $4$ .

$n > 8$ or $10 - 12 n > - 38$

Step 2

Simplify the second inequality.

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

Subtract $10$ from both sides of the inequality.

$n > 8$ or $- 12 n > - 38 - 10$

Subtract $10$ from $- 38$ .

$n > 8$ or $- 12 n > - 48$

Divide each term in $- 12 n > - 48$ by $- 12$ and simplify.

Divide each term in $- 12 n > - 48$ by $- 12$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$n > 8$ or $\frac{- 12 n}{- 12} < \frac{- 48}{- 12}$

Simplify the left side.

Cancel the common factor of $- 12$ .

Cancel the common factor.

$n > 8$ or $\frac{- 12 n}{- 12} < \frac{- 48}{- 12}$

Divide $n$ by $1$ .

$n > 8$ or $n < \frac{- 48}{- 12}$

Simplify the right side.

Divide $- 48$ by $- 12$ .

$n > 8$ or $n < 4$

Step 3

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

$n < 4$ or $n > 8$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$n < 4 or n > 8$

Interval Notation:

$(- \infty, 4) \cup (8, \infty)$

Step 5

Solve the System of Inequalities 12+4n>44 or 10-12n>-38

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