Solve the System of Inequalities 5<k-2<11

$5 < k - 2 < 11$

Step 1

Solve $5 < k - 2$ for $k$ .

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

$k - 2 > 5$

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

Add $2$ to both sides of the inequality.

$k > 5 + 2$

Add $5$ and $2$ .

$k > 7$

Step 2

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

Add $2$ to both sides of the inequality.

$k < 11 + 2$

Add $11$ and $2$ .

$k < 13$

Step 3

Find the intersection of $k > 7$ and $k < 13$ .

$7 < k < 13$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$7 < k < 13$

Interval Notation:

$(7, 13)$

Step 5