Solve the problem.
-When a number is subtracted from $- 7$, the absolute value of the difference is more than 3 . Use interval notation to express the set of all numbers that satisfy this condition.
A) $( - \infty , - 10 ) \cup ( - 4 , \infty )$
B) $( - \infty , - 4 ) \cup ( 10 , \infty )$
C) $( - \infty , - 10 ] \cup [ - 4 , \infty )$
D) $( - 10 , - 4 )$

Question

Quizplus · Accepted Answer

The condition can be expressed as $|x + 7| > 3$. Solving this inequality, we get two cases: $x + 7 > 3$ and $x + 7 < -3$. Solving these gives $x > -4$ and $x < -10$, respectively. Thus, the solution is $( - \infty , - 10 ) \cup ( - 4 , \infty )$.

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