Re-write 27 = 3

If the powers are equal, and the bases (here, 3) are equal
then the exponents must also be equal**:**

|2x - 5| = 3 |

Case 1: |2x - 5| = +(2x - 5) |

2x - 5 = 3 and thus x = 4

Case 2: |2x - 5| = -(2x - 5) |

-2x + 5 = 3 and thus x = 1

In summary, the original equation is solved by**:**

x = 1 or x = 2 or (in set notation): {1,2} |