Question : If $2x-4\leq \frac{2-x}{3}$ and $2(2x+5)>3x-5$, then $x$ can take which of the following values?
Option 1: –14
Option 2: 3
Option 3: 4
Option 4: 14
Correct Answer: –14
Solution :
Given: $2x-4\leq \frac{2–x}{3}$ and $2(2x+5)>3x-5$
Or, $3×(2x-4)\leq 2-x$ and $(4x+10)>3x-5$
Or, $(6x-12)\leq 2-x$ and $(4x-3x)>-5-10$
Or, $(6x+x)\leq 2+12$ and $(4x-3x)>-15$
Or, $7x\leq14$ and $x>-15$
Or, $x\leq2$ and $x>-15$
Or, $-15<x\leq2$
Amongst all the given values –14 satisfies the above condition.
Hence, the correct answer is –14.
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