Solve the inequations: 2|4-5 x| 9 - Vidyadip

Question

Solve the inequations: $2|4-5 x| \geq 9$

✓

Answer

$
\begin{aligned}
& 2|4-5 x| \geq 9 \\
& \therefore|4-5 x| \geq \frac{9}{2} \\
& \therefore 4-5 x \geq \frac{9}{2} \text { or } 4-5 x \leq-\frac{9}{2} \ldots . . .[|x| \geq \text { a implies } x \leq-a \text { or } x \geq a]
\end{aligned}
$
Subtracting 4 from both sides, we get
$
-5 x \geq \frac{1}{2} \text { or }-5 x \leq \frac{-17}{2}
$
Divide by -5 (so inequality sign changes)
$\therefore \mathrm{x} \leq-\frac{1}{10}$ or $\mathrm{x} \geq \frac{17}{10}$
$\therefore x$ takes all real values less than or equal to $-\frac{1}{10}$
or it takes all real values greater or equal to $\frac{17}{10}$.
$\therefore$ the solution set is $\left(-\infty,-\frac{1}{10}\right]$ or $\left[\frac{17}{10}, \infty\right)$

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