15≤3x10+1 lt;25 ⇒ 15≤3x+1010 lt;25 ⇒ 1≤3x+102 lt;2 ⇒ 2≤ 3x+10 lt;4 ⇒ 2 10≤ 3x lt;4 10 ⇒ 12≤ 3x lt; 6 ⇒ 4≤ ...

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Law of Reciprocal

Solve: -15≤3...

Question

Solve: $\frac{- 1}{5} \leq \frac{3 x}{10} + 1 < \frac{2}{5}$

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Solution

$\frac{- 1}{5} \leq \frac{3 x}{10} + 1 < \frac{2}{5}$
$\Rightarrow \frac{- 1}{5} \leq \frac{3 x + 10}{10} < \frac{2}{5}$
$\Rightarrow - 1 \leq \frac{3 x + 10}{2} < 2$
$\Rightarrow - 2 \leq 3 x + 10 < 4$
$\Rightarrow - 2 - 10 \leq 3 x < 4 - 10$
$\Rightarrow - 12 \leq 3 x < - 6$
$\Rightarrow - 4 \leq x < - 2$
$∴ x \in [- 4, - 2)$

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