Question:
Given A = |x+3 + |x-2| - |2x-8|. The maximum value of |A| is :
Given A = |x+3 + |x-2| - |2x-8|. The maximum value of |A| is :
Updated On: Aug 9, 2024
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The Correct Option is B
Solution and Explanation
To find the maximum value of |A|, we need to determine the values of x that give the largest absolute value of A. We can do this by analyzing the three absolute value expressions in the equation for A separately:
|x+3|: This expression is equal to x + 3 for x ≥ -3, and equal to -x - 3 for x < -3.
|x-2|: This expression is equal to x - 2 for x ≥ 2, and equal to -x + 2 for x < 2.
-|2x-8|: This expression is equal to -(2x - 8) for x ≤ 4, and equal to 2x-8 for x > 4.
Combining these cases, we can construct the following table of the possible values for A depending on the value of x:
x ≥ 4: A = (x + 3) + (x - 2) - (2x - 8) = 7
2 ≤ x < 4: A = (x + 3) + (x - 2) - (-2x + 8) = 4x - 7
-3 ≤ x < 2: A = (x + 3) - (x - 2) - (-2x + 8) = 2x - 3
x < -3: A = (-x - 3) + (-x + 2) - (-2x + 8) = -9
In all the cases, the maximum absolute value of A is 9.
Hence, the maximum value of |A| is 9.
So, option B is the correct answer.
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