Question : If $3x–3<3+\frac{x}{2}$ and $x–2\leq 6+2x$, then $x$ can take which of the following values?
Option 1: 6
Option 2: 2
Option 3: 10
Option 4: –10
Correct Answer: 2
Solution :
Given: $3x–3<3+\frac{x}{2}$ and $x–2\leq 6+2x$
Or, $3x–\frac{x}{2}<3+3$ and $–2–6\leq 2x–x$
Or, $\frac{6x–x}{2}<6$ and $–8\leq x$
Or, $\frac{5x}{2}<6$ and $–8\leq x$
Or, $5x<12$ 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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