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For a real number x the condition |3x - 20| + |3x - 40| = 20 necessarily holds if
- a)10 < x < 15
- b)7 < x < 12
- c)9 < x < 14
- d)6 < x < 11
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
For a real number x the condition |3x - 20| + |3x - 40| = 20necessaril...
Case 1: x ≥ 40/3
we get 3x-20 +3x-40 = 20
6x=80
Case 2
we get 3x - 20 + 40 - 3x = 20
we get 20 = 20
So we get x
Case 3x < 20/3
we get 20-3x+40-3x =20
40=6x
x = 20/3
but this is not possible
so we get from case 1,2 and 3
Now looking at options
we can say only option C satisfies for all x .
Hence 7<x<12.
Most Upvoted Answer
For a real number x the condition |3x - 20| + |3x - 40| = 20necessaril...
Understanding the Equation:
To understand why option 'B' (7 < x="" />< 12)="" is="" the="" correct="" answer,="" let's="" first="" analyze="" the="" given="" equation:="" |3x="" -="" 20|="" +="" |3x="" -="" 40|="20." this="" equation="" involves="" the="" absolute="" value="" of="" expressions="" containing="" />
Solving the Equation:
1. We first need to consider the two cases for the absolute value:
a) When 3x - 20 ≥ 0, then |3x - 20| = 3x - 20
b) When 3x - 20 < 0,="" then="" |3x="" -="" 20|="-(3x" -="" 20)="20" -="" />
2. Similarly, for the second absolute value:
a) When 3x - 40 ≥ 0, then |3x - 40| = 3x - 40
b) When 3x - 40 < 0,="" then="" |3x="" -="" 40|="-(3x" -="" 40)="40" -="" />
3. Now, we substitute these values back into the original equation and simplify:
(3x - 20) + (3x - 40) = 20
6x - 60 = 20
6x = 80
x = 80/6
x = 13.33
Checking the Options:
Now we need to check which option satisfies the condition 7 < x="" />< />
- If x is less than 7 or greater than 12, the equation will not hold true.
- Therefore, the correct range for x is 7 < x="" />< 12,="" making="" option="" 'b'="" the="" right="" />
Therefore, the correct answer is option 'B' (7 < x="" />< 12)="" for="" the="" equation="" |3x="" -="" 20|="" +="" |3x="" -="" 40|="20" to="" hold="" true.="" 12)="" for="" the="" equation="" |3x="" -="" 20|="" +="" |3x="" -="" 40|="20" to="" hold="" />
To understand why option 'B' (7 < x="" />< 12)="" is="" the="" correct="" answer,="" let's="" first="" analyze="" the="" given="" equation:="" |3x="" -="" 20|="" +="" |3x="" -="" 40|="20." this="" equation="" involves="" the="" absolute="" value="" of="" expressions="" containing="" />
Solving the Equation:
1. We first need to consider the two cases for the absolute value:
a) When 3x - 20 ≥ 0, then |3x - 20| = 3x - 20
b) When 3x - 20 < 0,="" then="" |3x="" -="" 20|="-(3x" -="" 20)="20" -="" />
2. Similarly, for the second absolute value:
a) When 3x - 40 ≥ 0, then |3x - 40| = 3x - 40
b) When 3x - 40 < 0,="" then="" |3x="" -="" 40|="-(3x" -="" 40)="40" -="" />
3. Now, we substitute these values back into the original equation and simplify:
(3x - 20) + (3x - 40) = 20
6x - 60 = 20
6x = 80
x = 80/6
x = 13.33
Checking the Options:
Now we need to check which option satisfies the condition 7 < x="" />< />
- If x is less than 7 or greater than 12, the equation will not hold true.
- Therefore, the correct range for x is 7 < x="" />< 12,="" making="" option="" 'b'="" the="" right="" />
Therefore, the correct answer is option 'B' (7 < x="" />< 12)="" for="" the="" equation="" |3x="" -="" 20|="" +="" |3x="" -="" 40|="20" to="" hold="" true.="" 12)="" for="" the="" equation="" |3x="" -="" 20|="" +="" |3x="" -="" 40|="20" to="" hold="" />
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For a real number x the condition |3x - 20| + |3x - 40| = 20necessarily holds ifa)10 < x < 15b)7 < x < 12c)9 < x < 14d)6 < x < 11Correct answer is option 'B'. Can you explain this answer? for CLAT 2025 is part of CLAT preparation. The Question and answers have been prepared according to the CLAT exam syllabus. Information about For a real number x the condition |3x - 20| + |3x - 40| = 20necessarily holds ifa)10 < x < 15b)7 < x < 12c)9 < x < 14d)6 < x < 11Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CLAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a real number x the condition |3x - 20| + |3x - 40| = 20necessarily holds ifa)10 < x < 15b)7 < x < 12c)9 < x < 14d)6 < x < 11Correct answer is option 'B'. Can you explain this answer?.
For a real number x the condition |3x - 20| + |3x - 40| = 20necessarily holds ifa)10 < x < 15b)7 < x < 12c)9 < x < 14d)6 < x < 11Correct answer is option 'B'. Can you explain this answer? for CLAT 2025 is part of CLAT preparation. The Question and answers have been prepared according to the CLAT exam syllabus. Information about For a real number x the condition |3x - 20| + |3x - 40| = 20necessarily holds ifa)10 < x < 15b)7 < x < 12c)9 < x < 14d)6 < x < 11Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CLAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a real number x the condition |3x - 20| + |3x - 40| = 20necessarily holds ifa)10 < x < 15b)7 < x < 12c)9 < x < 14d)6 < x < 11Correct answer is option 'B'. Can you explain this answer?.
Solutions for For a real number x the condition |3x - 20| + |3x - 40| = 20necessarily holds ifa)10 < x < 15b)7 < x < 12c)9 < x < 14d)6 < x < 11Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for CLAT.
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For a real number x the condition |3x - 20| + |3x - 40| = 20necessarily holds ifa)10 < x < 15b)7 < x < 12c)9 < x < 14d)6 < x < 11Correct answer is option 'B'. Can you explain this answer?, a detailed solution for For a real number x the condition |3x - 20| + |3x - 40| = 20necessarily holds ifa)10 < x < 15b)7 < x < 12c)9 < x < 14d)6 < x < 11Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of For a real number x the condition |3x - 20| + |3x - 40| = 20necessarily holds ifa)10 < x < 15b)7 < x < 12c)9 < x < 14d)6 < x < 11Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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