To solve the compound inequality [tex]\( p - 8 > 8 \)[/tex] or [tex]\( p + 7 < -3 \)[/tex], let's solve each inequality separately.
### Solving [tex]\( p - 8 > 8 \)[/tex]:
1. Start with the inequality:
[tex]\[
p - 8 > 8
\][/tex]
2. Add 8 to both sides to isolate [tex]\( p \)[/tex]:
[tex]\[
p - 8 + 8 > 8 + 8
\][/tex]
3. Simplify the inequality:
[tex]\[
p > 16
\][/tex]
So, the solution to the first inequality is:
[tex]\[
p > 16
\][/tex]
### Solving [tex]\( p + 7 < -3 \)[/tex]:
1. Start with the inequality:
[tex]\[
p + 7 < -3
\][/tex]
2. Subtract 7 from both sides to isolate [tex]\( p \)[/tex]:
[tex]\[
p + 7 - 7 < -3 - 7
\][/tex]
3. Simplify the inequality:
[tex]\[
p < -10
\][/tex]
So, the solution to the second inequality is:
[tex]\[
p < -10
\][/tex]
### Combining the Solutions:
The solutions to the inequalities are:
[tex]\[
p > 16 \quad \text{or} \quad p < -10
\][/tex]
Thus, the compound inequality solution for [tex]\( p \)[/tex] is:
[tex]\[
p > 16 \quad \text{or} \quad p < -10
\][/tex]
