Question

Which conjunction or disjunction is equivalent to the open sentence |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