Answer:
(x < -1) ∪ (6 < x)
Step-by-step explanation:
Divide by 3
|2x -5| > 7
"Unfold." That is, put the negative of the constant value on the other side of the absolute value expression, using the same inequality symbol.
-7 > 2x -5 > 7 . . . . . . . . . . this notation is convenient for expressing the two disjoint inequalities, but is not strictly correct because it is not true that -7 > 7.
Add 5, then divide by 2
-2 > 2x > 12
-1 > x > 6 . . . . . . . . . . this should be interpreted as -1 > x OR x > 6. Usually a compound inequality is interpreted as having an AND connector.
The solution is ...
(x < -1) ∪ (6 < x)
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The more correct (and less convenient) way to "unfold" the absolute value is to write it as two distinct inequalities:
Each of these is then separately solved (by adding 5 and dividing by 2) to get ...
