Question

solve the inequality
$3\leqslant 4 - 2x < 7$
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Answer 1

Answer:

$3 \leqslant 4 - 2x < 7 \\ add \: - 4 \: on \: all \: sides \\ 3 - 4 \leqslant 4 - 4 - 2x < 7 - 4 \\ - 1 \leqslant - 2x < 7 \\ taking \: ( - )sign \: < inequality \: change > \\ 1 \geqslant 2x > - 7 \\ divide \: 2 \: on \: all \: sides \\ \frac{1}{2} \geqslant x > \frac{7}{2}$

Answer 2

Question :-

solve the inequality :-

$\sf 3\leqslant 4 - 2x < 7$

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Solution :-

☆ Given Information :-

$\sf3 \leqslant 4 - 2x < 7$

☆ To Find :-

Solve the given inequality.

☆ Calculation :-

$: \implies \sf3 \leqslant 4 - 2x < 7$

$: \implies \sf3 - 4 \leqslant 2x < 7$

$: \implies \sf- 1 \leqslant 2x < 7$

$: \implies \sf 2x < 7 + 1$

$: \implies \sf 2x < 8$

$: \implies \sf x < \frac{8}{2}$

Cancelling, so as to get the lowest terms,

$: \implies \sf \: x < \frac{ \cancel{8} \: \: \: \tiny{4}}{ \cancel{2} \: \: \: \tiny{1}} = \frac{4}{1} = 4$

$: \implies \sf x < 4$

$\therefore \bf solution \: set = {3,2,1,0,- 1,- 2,- 3,...}$

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Final Answer :-

Solution Set = {3, 2, 1, 0, -1, -2, -3, ...}

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