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For inequality x^2 < 4, the solution set is -2 < x <2. ANSWER
Solved and completed.
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If you want more explanations, then consider that follows.
Inequality x^2 < 4 is the same as (is equivalent to) x^2 -4 < 0.
Factor left side x^2 - 4 = (x-2)*(x+2).
Therefore, your inequality is
(x-2)*(x+2) < = 0.
It happens if and only if the two factors (x-2) and (x+2) are of opposite (= different) signs, i.e.
x-2 < 0, x+2 > 0,
which implies
-2 < x < 2, ANSWER
the same answer set as in the very first solution above.
Solved, with complete explanations.