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Solve for $p$ . $\newline$ $7 \leq p + 18 \leq 15$ $\newline$ Write your answer as a compound inequality with integers. $\newline$ Choices: $\newline$ (A) $-11 \leq p \leq -3$ $\newline$ (B) $25 \leq p \leq 33$ $\newline$ (C) $-11 \leq p \leq 33$ $\newline$ (D) $25 \leq p \leq -3$

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Solve compound inequalities

Full solution

Q. Solve for

p

.

\newline

7 \leq p + 18 \leq 15

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

-11 \leq p \leq -3

\newline

(B)

25 \leq p \leq 33

\newline

(C)

-11 \leq p \leq 33

\newline

(D)

25 \leq p \leq -3

Isolate $p$ : To isolate $p$ , we need to subtract $18$ from all parts of the inequality because $p + 18$ involves addition of $18$ to $p$ .
Subtract $18$ : Subtract $18$ from all parts of the inequality: $\newline$ $7 \leq p + 18 \leq 15$ $\newline$ $7 - 18 \leq p + 18 - 18 \leq 15 - 18$ $\newline$ $-11 \leq p \leq -3$
Check Solution: Check the solution by substituting the boundary values for $p$ into the original inequality to ensure they satisfy the conditions: $\newline$ For $p = -11$ : $7 \leq -11 + 18 \leq 15$ which simplifies to $7 \leq 7 \leq 15$ , which is true. $\newline$ For $p = -3$ : $7 \leq -3 + 18 \leq 15$ which simplifies to $7 \leq 15 \leq 15$ , which is also true.

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