devhdesai6505
Answered

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The number of solutions of |x - 1| + |x - 3| = 2 is​

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mhanifa

Answer:

There are 3 intervals as following:

x ≤ 1

  • -(x - 1) - (x - 3) = 2
  • -2x + 4 = 2
  • 2x = 2
  • x = 1

1 ≤ x ≤3

  • (x - 1) - (x - 3) = 2
  • 2 = 2,
  • any value of x in the same interval

x ≥ 3

  • (x - 1) + (x - 3) = 2
  • 2x - 4 = 2
  • 2x = 6
  • x = 3

Combining the all, we get:

  • 1 ≤ x ≤3 or
  • x = [1, 3]
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