Question : If $7+3x>3+2x$; and $x+3(x-7)<5-x$; then $x$ can take which of the following values?
Option 1: –5
Option 2: 5
Option 3: 6
Option 4: –6
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Correct Answer: 5
Solution : Given: $7+3x > 3+2x$ and $x+3(x-7) < 5-x$ $7+3x > 3+2x$ $⇒3x-2x > 3-7$ $⇒x > -4$ Also, $ x+3(x-7) < 5-x$ $⇒x+3x-21 < 5-x$ $⇒5x < 5+21$ $⇒x < \frac{26}{5}$ $⇒x < 5.2$ So, the value of $x$ lies between $-4 < x < 5.2$ Hence, the correct answer is 5.
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