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12 Dec 2024, 13:30
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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02 Jan 2025, 23:35
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It is given that
|2x−5|≤7
Case 1 : If value inside mod is positive or 0, it will give it out as it is. Hence, if 2x - 5 > 0 or 2x - 5 =0 then 2x-5 ≤ 7
Case 2 : If value inside mod is negative, it will give out only the magnitude. Hence, if 2x-5 < 0 then - (2x -5) ≤ 7
if we multiply both sides by -1 we get, 2x - 5 > or = -7 (Concept - If both sides of inequality are multiplied by the same negative value, inequality REVERSES)
Hence we get, -7 ≤ 2x -5 ≤ 7
Adding 5 to all terms
-7 +5 ≤ 2x - 5 + 5 ≤ 7 + 5 (Concept - If a constant is added to both sides of an inequality, inequality REMAINS SAME)
-2 ≤ 2x ≤ 12
Dividing by 2 we get
-1 ≤ x ≤ 6 (Concept - If both sides of inequality are multiplied/ divided by the same positive value, inequality REMAINS SAME)
As x can take any value from -1 to 6 there values less than 3 (2, - 0.5, 0) are possible as well as values more than 3 (3.5, 5, 5.25) are also possible.
Hence, the data is not sufficient to compare quantity A with quantity B. Hence, Answer is D.
|2x−5|≤7
Case 1 : If value inside mod is positive or 0, it will give it out as it is. Hence, if 2x - 5 > 0 or 2x - 5 =0 then 2x-5 ≤ 7
Case 2 : If value inside mod is negative, it will give out only the magnitude. Hence, if 2x-5 < 0 then - (2x -5) ≤ 7
if we multiply both sides by -1 we get, 2x - 5 > or = -7 (Concept - If both sides of inequality are multiplied by the same negative value, inequality REVERSES)
Hence we get, -7 ≤ 2x -5 ≤ 7
Adding 5 to all terms
-7 +5 ≤ 2x - 5 + 5 ≤ 7 + 5 (Concept - If a constant is added to both sides of an inequality, inequality REMAINS SAME)
-2 ≤ 2x ≤ 12
Dividing by 2 we get
-1 ≤ x ≤ 6 (Concept - If both sides of inequality are multiplied/ divided by the same positive value, inequality REMAINS SAME)
As x can take any value from -1 to 6 there values less than 3 (2, - 0.5, 0) are possible as well as values more than 3 (3.5, 5, 5.25) are also possible.
Hence, the data is not sufficient to compare quantity A with quantity B. Hence, Answer is D.
