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Solve for $q$ . $\newline$ $q + 15 < 19$ or $q - 6 \geq 4$ $\newline$ Write your answer as a compound inequality with integers. $\newline$ Choices: $\newline$ (A) $4 \leq q \leq 10$ $\newline$ (B) $4 < q \leq 10$ $\newline$ (C) $q \leq 4$ or $q \geq 10$ $\newline$ (D) $q < 4$ or $q \geq 10$

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Solve compound inequalities

Full solution

Q. Solve for

q

.

\newline

q + 15 < 19

or

q - 6 \geq 4

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

4 \leq q \leq 10

\newline

(B)

4 < q \leq 10

\newline

(C)

q \leq 4

or

q \geq 10

\newline

(D)

q < 4

or

q \geq 10

Solve first inequality: First, let's solve the inequality $q + 15 < 19$ . To isolate $q$ , we need to subtract $15$ from both sides of the inequality. $q + 15 - 15 < 19 - 15$ $q < 4$
Solve second inequality: Now, let's solve the inequality $q - 6 \geq 4$ . $\newline$ To isolate $q$ , we need to add $6$ to both sides of the inequality. $\newline$ $q - 6 + 6 \geq 4 + 6$ $\newline$ $q \geq 10$
Final result: We have two separate inequalities from the original compound inequality: $\newline$ $q < 4$ or $q \geq 10$ $\newline$ This means $q$ can be any value less than $4$ or any value greater than or equal to $10$ .

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