Question

I'll fan and give a medal! :)
Which conjunction or disjunction is equivalent to the open sentence 4 – 2|n + 6| ≥ 2?

A.
n > –5 or n < –7

B.
n + 6 ≤ 1 and n + 6 ≥ –1

C.
–5 < n or n < –7

D.
n + 6 ≤ –1 and n + 6 ≥ 1

Answer 1

@KirbyLegs

Answer 2

@amoodarya @KirbyLegs

Answer 3

@jdoe0001

Answer 4

\(\bf 4 - 2|n + 6| \ge 2\implies - 2|n + 6|\ge 2+4 \implies - 2|n + 6|\ge -2\\ \quad \\
\textit{notice, we'll multiply by a negative value,thus } \color{red}{\textit{flipping the sign}}\\ \quad \\
- 2|n + 6|\ge -2\implies |n+6|\le \cfrac{-2}{-2}\implies |n+6|\le 1\\ \quad \\

|n+6|\le 1\implies
\begin{cases}
+(n+6)\le 1\implies n+6\le 1\\ \quad \\
\bf -(n+6)\le 1\implies n+6\ge -1
\end{cases}
\)

Answer 5

So the answer is D, correct?

Answer 6

@jdoe0001