Question

Will fan and give medal :)

Which conjunction or disjunction is equivalent to the open sentence |a – 9| ≤ 4.

A.
a – 9 ≥ 4 and a – 9 ≤ –4

B.
a – 9 ≤ 4 or a – 9 ≥ –4

C.
a – 9 ≤ 4 and a – 9 ≤ –4

D.
a – 9 ≤ 4 and a – 9 ≥ –4

Answer 1

recall that \(\bf |something| \le whatever\implies
\begin{cases}
+something \le whatever\\ \quad \\
\bf -something \le whatever
\end{cases}\)

Answer 2

okay...

Answer 3

@amoodarya

Answer 4

I still don't understand...

Answer 5

@KirbyLegs

Answer 6

when multiplying for a negative value, in inequalities, you'd have to "flip" the inequality sign as well, so \(\bf |something| \le whatever\\ \quad \\\implies
\begin{cases}
+something \le whatever\\ \quad \\
\bf -something \le whatever\implies something \ge -whatever
\end{cases}\)

plug in your values given in \(\bf |a-9|\le 4\) and see what you get

Answer 7

okay thanks :)

Answer 8

yw