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Solve for $p$ . $\newline$ $0 < p + 16 < 13$ $\newline$ Write your answer as a compound inequality with integers. $\newline$ Choices: $\newline$ (A) $p < -16$ or $p \geq -3$ $\newline$ (B) $-16 < p \leq -3$ $\newline$ (C) $-16 < p < -3$ $\newline$ (D) $p < -16$ or $p > -3$

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Solve advanced linear inequalities

Full solution

Q. Solve for

p

.

\newline

0 < p + 16 < 13

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

p < -16

or

p \geq -3

\newline

(B)

-16 < p \leq -3

\newline

(C)

-16 < p < -3

\newline

(D)

p < -16

or

p > -3

Isolate $p$ in compound inequality: First, we will isolate $p$ in the compound inequality by subtracting $16$ from all three parts of the inequality. $\newline$ $0 < p + 16 < 13$ $\newline$ $0 - 16 < p + 16 - 16 < 13 - 16$ $\newline$ $-16 < p < -3$
Identify range for $p$ : Now that we have isolated $p$ , we can see that $p$ must be greater than $-16$ and less than $-3$ . This matches one of the given choices.

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