Question

Which conjunction or disjunction is equivalent to the open sentence 4 – 2|n + 6| ≥ 2? A.
–5 < n or n < –7

B.
n + 6 ≤ 1 and n + 6 ≥ –1

C.
n + 6 ≤ –1 and n + 6 ≥ 1

D.
n > –5 or n < –7

Answer 1

\(\bf 4 - 2|n + 6| \ge 2\implies -2|n + 6| \ge 2+4\implies -2|n + 6| \ge 6\\ \quad \\
\textit{recall, in an inequality multiplying/dividing/exponentializing}\\
\textit{ by a negative number, we have to }flip \textit{ the inequality sign}\qquad thus\\ \quad \\
\cfrac{-2|n + 6|}{-2} \ge \cfrac{6}{-2}\implies |n+6|\le -3\\ \quad \\
|n+6|\le -3\implies
\begin{cases}
+(n+6)\le -3\\ \quad \\
\bf -(n+6)\le -3
\end{cases}\)


solve those 2 scenarios, what do they give you?

again, do not forget to "flip the inequality" sign when multiplying or dividing or exponentializing by a NEGATIVE number

Answer 2

wow thats amazing thank you so much that helps so much thank you

Answer 3

yw