Question : If $2 x - 4 \leq \frac{2 - x}{3}$ and $2 (2 x + 5) > 3 x - 5$ , then $x$ can take which of the following values?
Option 1: –14
Option 2: 3
Option 3: 4
Option 4: 14

Question

Question : If $3 x - 3 < 3 + \frac{x}{2}$ and $x - 2 \leq 6 + 2 x$ , then $x$ can take which of the following values?
Option 1: 6
Option 2: 2
Option 3: 10
Option 4: –10

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Answer 1

Correct Answer: –14

Solution : Given: $2 x - 4 \leq \frac{2 - x}{3}$ and $2 (2 x + 5) > 3 x - 5$
Or, $3 \times (2 x - 4) \leq 2 - x$ and $(4 x + 10) > 3 x - 5$
Or, $(6 x - 12) \leq 2 - x$ and $(4 x - 3 x) > - 5 - 10$
Or, $(6 x + x) \leq 2 + 12$ and $(4 x - 3 x) > - 15$
Or, $7 x \leq 14$ and $x > - 15$
Or, $x \leq 2$ and $x > - 15$
Or, $- 15 < x \leq 2$
Amongst all the given values –14 satisfies the above condition.
Hence, the correct answer is –14.

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Question : If 2x−4≤2−x3 and 2(2x+5)>3x−5, then x can take which of the following values?Option 1: –14Option 2: 3Option 3: 4Option 4: 14

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Question : If $2 x - 4 \leq \frac{2 - x}{3}$ and $2 (2 x + 5) > 3 x - 5$ , then $x$ can take which of the following values?
Option 1: –14
Option 2: 3
Option 3: 4
Option 4: 14