Intermediate Algebra, Chapter 2, 2.7 summary exercises, Section 2.7, Problem 46

Evaluate the inequality $|x + 2| < -3$. Then give the solution in interval notation.

By using the property of Absolute value, we have

$
\begin{equation}
\begin{aligned}
x + 2 &< - 3 && \text{and} & x + 2 &> - (-3)\\
\\
x + 2 &< -3 && \text{and} & x + 2 &> 3\\
\\
x &< -5 && \text{and} & x &> 1
\end{aligned}
\end{equation}
$

Since the two inequalities are joined by $and$, then we need to find the intersection of the two.
However, both inequalities will not intersect at any interval because they move in opposite direction. Thus,
the solution is an empty set or $\cancel{0}$.

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