Question

7. Solve 7x+3<5x+12, x ∈ I.​

Answer 1

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Step-by-step explanation:

1 min

Answer 2

$\large\underline{\sf{Solution-}}$

Given that

$\rm :\longmapsto\:7x + 3 < 5x + 12$

On Subtracting 5x from both sides, we get

$\rm :\longmapsto\:7x + 3 - 5x< 5x + 12 - 5x$

$\rm :\longmapsto\:2x + 3 <12$

On Subtracting 3 from each term, we get

$\rm :\longmapsto\:2x + 3 - 3<12 - 3$

$\rm :\longmapsto\:2x <9$

$\rm :\longmapsto\:x <\dfrac{9}{2}$

$\rm :\longmapsto\:x <4.5$

$\rm :\longmapsto\:As \: x\: \in \: I$

$\bf\implies \:x \: = \: \{..., - 2, - 1,0,1,2,3,4 \}$

Additional information :-

$\rm :\longmapsto\:A > B\rm \implies\: - A < - B$

$\rm :\longmapsto\:A \geqslant B\rm \implies\: - A \leqslant - B$

$\rm :\longmapsto\:A < B\rm \implies\: - A > - B$

$\rm :\longmapsto\:A \leqslant B\rm \implies\: - A \geqslant - B$

$\rm :\longmapsto\:A > - B\rm \implies\: - A < B$

$\rm :\longmapsto\:A < - B\rm \implies\: - A > B$