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Solve for $q$ . $\newline$ $q + 20 \leq 14$ or $q + 16 \geq 20$ $\newline$ Write your answer as a compound inequality with integers. $\newline$ Choices: $\newline$ (A) $q \leq -6$ or $q \geq 4$ $\newline$ (B) $q \leq 34$ or $q \geq 36$ $\newline$ (C) $q \leq 34$ or $q \geq 4$ $\newline$ (D) $q \leq -6$ or $q \geq 36$

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Solve compound inequalities

Full solution

Q. Solve for

q

.

\newline

q + 20 \leq 14

or

q + 16 \geq 20

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

q \leq -6

or

q \geq 4

\newline

(B)

q \leq 34

or

q \geq 36

\newline

(C)

q \leq 34

or

q \geq 4

\newline

(D)

q \leq -6

or

q \geq 36

First Inequality Solution: We have two separate inequalities to solve: $q + 20 \leq 14$ and $q + 16 \geq 20$ . Let's start with the first inequality, $q + 20 \leq 14$ . $\newline$ To isolate $q$ , we need to subtract $20$ from both sides of the inequality. $\newline$ $q + 20 - 20 \leq 14 - 20$ $\newline$ $q \leq -6$
Second Inequality Solution: Now let's solve the second inequality, $q + 16 \geq 20$ . To isolate $q$ , we subtract $16$ from both sides of the inequality. $q + 16 - 16 \geq 20 - 16$ $q \geq 4$
Compound Inequality Solution: We have now solved both inequalities. The solution to the compound inequality is: $q \leq -6$ or $q \geq 4$

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