To solve the compound inequality [tex]\( k+18 > 12 \)[/tex] or [tex]\( k+16 < 9 \)[/tex], let's break it down step by step.
### Step 1: Solve the first inequality [tex]\( k + 18 > 12 \)[/tex]
1.1. Subtract 18 from both sides of the inequality [tex]\( k + 18 > 12 \)[/tex]:
[tex]\[
k + 18 - 18 > 12 - 18
\][/tex]
1.2. Simplify the expression:
[tex]\[
k > -6
\][/tex]
### Step 2: Solve the second inequality [tex]\( k + 16 < 9 \)[/tex]
2.1. Subtract 16 from both sides of the inequality [tex]\( k + 16 < 9 \)[/tex]:
[tex]\[
k + 16 - 16 < 9 - 16
\][/tex]
2.2. Simplify the expression:
[tex]\[
k < -7
\][/tex]
### Step 3: Combine the inequalities
The solution is a combination of the two inequalities found:
[tex]\[
k > -6 \text{ or } k < -7
\][/tex]
Thus, the compound inequality is:
[tex]\[
k > -6 \text{ or } k < -7
\][/tex]
This means that [tex]\( k \)[/tex] can be any value greater than [tex]\(-6\)[/tex] or any value less than [tex]\(-7\)[/tex], representing two separate regions on the number line.
