Solve the System of Inequalities 2n+7>=27 or 3+3n<=30

$2 n + 7 \geq 27$ or $3 + 3 n \leq 30$

Step 1

Simplify the first inequality.

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

Subtract $7$ from both sides of the inequality.

$2 n \geq 27 - 7$

Subtract $7$ from $27$ .

$2 n \geq 20$

Divide each term in $2 n \geq 20$ by $2$ and simplify.

Divide each term in $2 n \geq 20$ by $2$ .

$\frac{2 n}{2} \geq \frac{20}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 n}{2} \geq \frac{20}{2}$

Divide $n$ by $1$ .

$n \geq \frac{20}{2}$

Simplify the right side.

Divide $20$ by $2$ .

$n \geq 10$

Step 2

Simplify the second inequality.

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

Subtract $3$ from both sides of the inequality.

$3 n \leq 30 - 3$

Subtract $3$ from $30$ .

$3 n \leq 27$

Divide each term in $3 n \leq 27$ by $3$ and simplify.

Divide each term in $3 n \leq 27$ by $3$ .

$\frac{3 n}{3} \leq \frac{27}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 n}{3} \leq \frac{27}{3}$

Divide $n$ by $1$ .

$n \leq \frac{27}{3}$

Simplify the right side.

Divide $27$ by $3$ .

$n \leq 9$

Step 3

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

$n \leq 9$ or $n \geq 10$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$n \leq 9 or n \geq 10$

Interval Notation:

$(- \infty, 9] \cup [10, \infty)$

Step 5

Solve the System of Inequalities 2n+7>=27 or 3+3n<=30

Related Questions

Support LCMGCF.com by disabling your adblocker.