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x^{2}-9<0
Multiply the inequality by -1 to make the coefficient of the highest power in -x^{2}+9 positive. Since -1 is negative, the inequality direction is changed.
x^{2}<9
Add 9 to both sides.
x^{2}<3^{2}
Calculate the square root of 9 and get 3. Rewrite 9 as 3^{2}.
|x|<3
Inequality holds for |x|<3.
x\in \left(-3,3\right)
Rewrite |x|<3 as x\in \left(-3,3\right).