Question

Absolute Value Equations and Inequalities?

Please help!

1.

Which conjunction or disjunction is equivalent to the open sentence |a – 8| ≤ 3.

A.
a – 8 ≤ 3 and a – 8 ≥ –3

B.
a – 8 ≥ 3 and a – 8 ≤ –3

C.
a – 8 ≤ 3 or a – 8 ≥ –3

D.
a – 8 ≥ 3 or a – 8 ≤ –3

Answer 1

you know |8-a|=|a-8|
that is better
now you may know |x|<k --> -k<x<k

so |a-8|<=3
-3<=a-8<=3
8-3<=a<=3+8
can you go on?

Answer 2

\[\left| x-a \right|\le b,-b \le x-a \le b\]
\[\left| x-a \right|\ge b,x-a \le -b and x-a \ge b\]