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Solve for $p$ . $\newline$ $p - 5 \leq 1$ or $p + 6 \geq 15$ $\newline$ Write your answer as a compound inequality with integers. $\newline$ Choices: $\newline$ (A) $p \leq 6$ or $p \geq 21$ $\newline$ (B) $p \leq -4$ or $p \geq 9$ $\newline$ (C) $p \leq -4$ or $p \geq 21$ $\newline$ (D) $p \leq 6$ or $p \geq 9$

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Solve compound inequalities

Full solution

Q. Solve for

p

.

\newline

p - 5 \leq 1

or

p + 6 \geq 15

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

p \leq 6

or

p \geq 21

\newline

(B)

p \leq -4

or

p \geq 9

\newline

(C)

p \leq -4

or

p \geq 21

\newline

(D)

p \leq 6

or

p \geq 9

Solve First Part: Solve the first part of the compound inequality. $\newline$ We have $p - 5 \leq 1$ . To isolate $p$ , we need to add $5$ to both sides of the inequality. $\newline$ $p - 5 + 5 \leq 1 + 5$ $\newline$ $p \leq 6$
Solve Second Part: Solve the second part of the compound inequality. $\newline$ We have $p + 6 \geq 15$ . To isolate $p$ , we need to subtract $6$ from both sides of the inequality. $\newline$ $p + 6 - 6 \geq 15 - 6$ $\newline$ $p \geq 9$
Combine Solutions: Combine the solutions from Step $1$ and Step $2$ to form the compound inequality. $\newline$ The solution is $p \leq 6$ or $p \geq 9$ .

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