Question : If $2 x - 2 (x - 2) < 5 - x > - 2 x + 2$ , then the value of $x$ is:
Option 1: 0
Option 2: 2
Option 3: 3
Option 4: –4

Question

Question : If $2 x - 2 (3 + 4 x) < - 1 - 2 x > \frac{- 5}{3} - \frac{x}{3}$ ; then $x$ can take which of the following values?
Option 1: 1
Option 2: 2
Option 3: –2
Option 4: –1

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Answer 1

Correct Answer: 0

Solution : Given: $2 x - 2 (x - 2) < 5 - x > - 2 x + 2$
$\Rightarrow 2 x - 2 (x - 2) < 5 - x$ and $5 - x > - 2 x + 2$
$\Rightarrow 2 x - 2 x + 4 < 5 - x$
$\Rightarrow - 1 < - x$
Now, multiply both sides by –1 (which reverses the inequality), we get:
$∴ x < 1$
Also, $5 - x > - 2 x + 2$
$\Rightarrow 5 > - x - 2 x + 2$
$\Rightarrow 5 > - 3 x + 2$
$\Rightarrow 3 > - 3 x$
Divide both sides by −3. (Dividing by a negative number, reverses the inequality.)
$∴ x > - 1$
So, the range of $x$ is $- 1 < x < 1$ .
Hence, the correct answer is 0.

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Question : If 2x−2(x−2)<5−x>−2x+2, then the value of x is:Option 1: 0Option 2: 2Option 3: 3Option 4: –4

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Question : If $2 x - 2 (x - 2) < 5 - x > - 2 x + 2$ , then the value of $x$ is:
Option 1: 0
Option 2: 2
Option 3: 3
Option 4: –4