Solve for y
y\in \begin{bmatrix}-2\sqrt{3},2\sqrt{3}\end{bmatrix}
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-12+y^{2}\leq 0
Multiply the inequality by -1 to make the coefficient of the highest power in 12-y^{2} positive. Since -1 is negative, the inequality direction is changed.
y^{2}\leq 12
Add 12 to both sides.
y^{2}\leq \left(2\sqrt{3}\right)^{2}
Calculate the square root of 12 and get 2\sqrt{3}. Rewrite 12 as \left(2\sqrt{3}\right)^{2}.
|y|\leq 2\sqrt{3}
Inequality holds for |y|\leq 2\sqrt{3}.
y\in \begin{bmatrix}-2\sqrt{3},2\sqrt{3}\end{bmatrix}
Rewrite |y|\leq 2\sqrt{3} as y\in \left[-2\sqrt{3},2\sqrt{3}\right].
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