Possible Value of |−X| − X2 When |−2X + 9| = 3
Absolute value equations often produce more than one solution.
In this problem, we solve the equation |−2X + 9| = 3
and determine the possible value of |−X| − X2
by checking each case carefully.
Given
If |−2X + 9| = 3, find the possible value of:
|−X| − X2
Step 1: Solve the Absolute Value Equation
|−2X + 9| = 3 gives two cases:
Case 1
−2X + 9 = 3
−2X = −6
X = 3
Case 2
−2X + 9 = −3
−2X = −12
X = 6
Possible values of X: 3 and 6
Step 2: Substitute Values in |−X| − X2
For X = 3
|−3| − 32 = 3 − 9 = −6
Result: Not given in options
For X = 6
|−6| − 62 = 6 − 36 = −30
Result: Matches option
Final Answer
Correct Option: (B) −30
Conclusion
Absolute value equations should always be solved by considering
both positive and negative cases. After solving, substitute
each value into the required expression to find the correct answer.
