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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