Solve : 1 ≥ 15 – 7x > 2x – 27, x ∈ N - Vidyadip

Question

Solve : 1 ≥ 15 – 7x > 2x – 27, x ∈ N

✓

Answer

$
\begin{aligned}
& 1 \geq 15-7 x>2 x-27 \\
& 1 \geq 15-7 x \text { and } 15-7 x>2 x-27 \\
& \Rightarrow 7 x \geq 15-1 \text { and }-7 x-2 x>-27-15 \\
& \Rightarrow 7 x \geq 14 \text { and }-9 x>-42 \\
& \Rightarrow x \geq 2 \text { and }-x>-\frac{42}{9} \\
& \Rightarrow 2 \leq x \text { and }-x>-\frac{14}{3} \text { and } x<\frac{14}{3} \\
& 2 \leq x<\frac{14}{3}
\end{aligned}
$
But $x \in N$
$\therefore$ Solution set $=\{2,3,4\}$.

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