Question

If X ∈ I ,then the solution set of the in equation 1< 3x+5 ≤ 11 is

Answer 1

$Given \: x\in I , then \:the \: solution \:set \:of$

$the \: inequality \: 1 \lt 3x+5\leq 11$

/* Subtract 5, we get */

$\implies 1-5 \lt 3x+5-5\leq 11 -5$

$\implies -4 \lt 3x\leq 6$

$\implies \frac{-4}{3} \lt \frac{3x}{3} \leq \frac{6}{3}$

$\implies \frac{-4}{3} \lt x \leq 2$

$\implies -1.\bar {3} \lt x \leq 2$

$\pink { x \in I }$

Therefore.,

$\green { Solution \:set } \green { \{ -1 ,0, 1,2 \}}$

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