The easiest way to verify if a satisfies the two given inequalities is by rewriting the absolute value inequality as a compound inequality.
|x+3|≥8
Since the absolute value is greater than or equal to 8, we can rewrite this absolute value inequality as an or compound inequality.
x+3≥8 or x+3≤-8
Notice that one of the inequalities is the opposite of the given inequality. This means that an arbitrary number a cannot satisfy both inequalities. We will verify this by supposing that x= -12. In the compound inequality, this value satisfies the second inequality:
-12+3≤-8 ⇒ -9≤-8 ✓
However, it does not satisfy the other inequality.
-12+3? ≥-8 ⇒ -9 ≱-8 *
Therefore, the statement is false.
