Question

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

The absolute value inequality is equivalent to
±(a - 9) ≤ 4
When the minus sign is chosen and the expression is multiplied by -1, the comparison operator is reversed and the expression becomes
a - 9 ≥ -4

The solution spaces of
a - 9 ≤ 4
a - 9 ≥ -4
overlap, so the solution is the conjunction of the two inequalities. This matches selection ...
D. a - 9 ≤ 4 and a - 9 ≥ -4