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Solve for $q$ . $\newline$ $q + 18 \leq 4$ or $q - 5 > 10$ $\newline$ Write your answer as a compound inequality with integers. $\newline$ Choices: $\newline$ (A) $q \leq 22$ or $q > 15$ $\newline$ (B) $q \leq 22$ or $q > 5$ $\newline$ (C) $q \leq -14$ or $q > 5$ $\newline$ (D) $q \leq -14$ or $q > 15$

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Solve compound inequalities

Full solution

Q. Solve for

q

.

\newline

q + 18 \leq 4

or

q - 5 > 10

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

q \leq 22

or

q > 15

\newline

(B)

q \leq 22

or

q > 5

\newline

(C)

q \leq -14

or

q > 5

\newline

(D)

q \leq -14

or

q > 15

Isolate $q$ in first part: Solve the first part of the compound inequality. $\newline$ We have $q + 18 \leq 4$ . To isolate $q$ , we need to subtract $18$ from both sides of the inequality. $\newline$ $q + 18 - 18 \leq 4 - 18$ $\newline$ $q \leq -14$
Isolate q in second part: Solve the second part of the compound inequality. $\newline$ We have $q - 5 > 10$ . To isolate q, we need to add $5$ to both sides of the inequality. $\newline$ $q - 5 + 5 > 10 + 5$ $\newline$ $q > 15$
Combine solutions for final inequality: Combine the solutions from Step $1$ and Step $2$ to write the final compound inequality. $\newline$ The solution is $q \leq -14$ or $q > 15$ .

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