For a real number x the condition |3x - 20| + |3x - 40| = 20 necessarily holds if
Explanation:
Case 1: 3x ≥ 40 ⇒ x ≥ 13.33
⇒ 3x – 20 + 3x – 40 = 20
⇒ 6x = 80
⇒ x = 13.33
Case 2: 20 ≤ 3x < 40 ⇒ 6.67 ≤ x < 13.33
⇒ 3x – 20 - 3x + 40 = 20
⇒ 20 = 20
This is always true.
Case 3: 3x ≤ 20
⇒ - 3x + 20 - 3x + 40 = 20
⇒ -6x = -40
⇒ x = 6.67
Combining solution from all the three cases, we get
6.67 ≤ x ≤ 13.33
Only option (d) is a subset of this range.
Hence, option (d).
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