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

Question

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

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Answer 1

Correct Answer: 2

Solution : Given: $3 x - 3 < 3 + \frac{x}{2}$ and $x - 2 \leq 6 + 2 x$
Or, $3 x - \frac{x}{2} < 3 + 3$ and $- 2 - 6 \leq 2 x - x$
Or, $\frac{6 x - x}{2} < 6$ and $- 8 \leq x$
Or, $\frac{5 x}{2} < 6$ and $- 8 \leq x$
Or, $5 x < 12$ and $- 8 \leq x$
Or, $x < \frac{12}{5}$ and $- 8 \leq x$
Or, $- 8 \leq x < 2.4$
Amongst all the given values, 2 satisfies the above condition.
Hence, the correct answer is 2.

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Question : If 3x–3<3+x2 and x–2≤6+2x, then x can take which of the following values?Option 1: 6Option 2: 2Option 3: 10Option 4: –10

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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