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Solve for [tex]$p$[/tex].

[tex]\[ p - 8 \ \textgreater \ 8 \quad \text{or} \quad p + 7 \ \textless \ -3 \][/tex]

Write your answer as a compound inequality:
[tex]\[\boxed{\phantom{p \ \textgreater \ 16}} \quad \text{or} \quad \boxed{\phantom{p \ \textless \ -10}}\][/tex]

Sagot :

GinnyAnsweridn
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]
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