Solve the inequations: |2 x+7| 25 - Vidyadip

Question

Solve the inequations: $|2 x+7| \leq 25$

✓

Answer

$
\begin{aligned}
& |2 x+7|<25 \\
& \therefore-25 \leq 2 x+7 \leq 25 \ldots . .[|x| \leq \text { a implies }-a \leq x \leq a]
\end{aligned}
$
Subtracting 7 from both sides, we get
$-32 \leq 2 x \leq 18$
Dividing by 2 on both sides, we get
$-16 \leq \mathrm{x} \leq 9$
$\therefore x$ can take all real values between -16 and 9 including -16 and 9 .
$\therefore$ the solution set is $[-16,9]$

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