Question : If $7 + 3 x > 3 + 2 x$ ; 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

Question

Question : If $4 (2 x + 3) > 5 - x$ and $5 x - 3 (2 x - 7) > 3 x - 1,$ then $x$ can take which of the following values?
Option 1: 6
Option 2: –1
Option 3: 5
Option 4: –6

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Answer 1

Correct Answer: 5

Solution : Given: $7 + 3 x > 3 + 2 x$ and $x + 3 (x - 7) < 5 - x$
$7 + 3 x > 3 + 2 x$
$\Rightarrow 3 x - 2 x > 3 - 7$
$\Rightarrow x > - 4$
Also, $x + 3 (x - 7) < 5 - x$
$\Rightarrow x + 3 x - 21 < 5 - x$
$\Rightarrow 5 x < 5 + 21$
$\Rightarrow x < \frac{26}{5}$
$\Rightarrow x < 5.2$
So, the value of $x$ lies between $- 4 < x < 5.2$
Hence, the correct answer is 5.

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Question : If 7+3x>3+2x; and x+3(x−7)<5−x; then x can take which of the following values?Option 1: –5Option 2: 5Option 3: 6Option 4: –6

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Question : If $7 + 3 x > 3 + 2 x$ ; 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