Solve the System of Inequalities 15<x+8 and x+8<=19

$15 < x + 8$ and $x + 8 \leq 19$

Step 1

Simplify the first inequality.

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

$x + 8 > 15$ and $x + 8 \leq 19$

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

Subtract $8$ from both sides of the inequality.

$x > 15 - 8$ and $x + 8 \leq 19$

Subtract $8$ from $15$ .

$x > 7$ and $x + 8 \leq 19$

Step 2

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

Subtract $8$ from both sides of the inequality.

$x > 7$ and $x \leq 19 - 8$

Subtract $8$ from $19$ .

$x > 7$ and $x \leq 11$

Step 3

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

$7 < x \leq 11$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$7 < x \leq 11$

Interval Notation:

$(7, 11]$

Step 5