Solve the inequations: 2|x+3|>1 - Vidyadip

Question

Solve the inequations: $2|x+3|>1$

✓

Answer

$
2|x+3|>1
$
Dividing by 2 on both sides, we get
$
\begin{aligned}
& |x+3|>\frac{1}{2} \\
& \therefore x+3<-\frac{1}{2} \text { or } x+3>\frac{1}{2} \ldots . .[|x|>\text { a implies } x<-a \text { or } x>a]
\end{aligned}
$
Subtracting 3 from both sides, we get
$
\begin{aligned}
& x<-3-\frac{1}{2} \text { or } x>-3+\frac{1}{2} \\
& \therefore x<\frac{-7}{2} \text { or } x>\frac{-5}{2}
\end{aligned}
$
$\therefore x$ can take all real values less $\frac{-7}{2}$ or it can take values greater than $\frac{-5}{2}$.
$\therefore$ Solution set is $\left(-\infty, \frac{-7}{2}\right) \cup\left(\frac{-7}{2}, \infty\right)$

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