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