Starting equation: |2x - 3| = 1
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Case 1: |2x - 3| = +(2x - 3) |
In this case, the starting equation states:
2x - 3 = 1
2x = 1 + 3 = 2
x = 2
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Case 2: |2x - 3| = -(2x - 3) |
In this case, the starting equation states:
-2x + 3 = 1
-2x = 1 - 3 = -2
x = 1
Putting together the two above cases,
the solution set for
|2x - 3| = 1 is:
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x = 1 or x = 2 or (in set notation): {1,2} |
Footnote: the equation "|2x - 3| = -1" has no solution