Solve for x
x\in \begin{bmatrix}-\frac{5}{3},\frac{5}{3}\end{bmatrix}
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-100+36x^{2}\leq 0
Multiply the inequality by -1 to make the coefficient of the highest power in 100-36x^{2} positive. Since -1 is negative, the inequality direction is changed.
x^{2}\leq \frac{25}{9}
Add \frac{25}{9} to both sides.
x^{2}\leq \left(\frac{5}{3}\right)^{2}
Calculate the square root of \frac{25}{9} and get \frac{5}{3}. Rewrite \frac{25}{9} as \left(\frac{5}{3}\right)^{2}.
|x|\leq \frac{5}{3}
Inequality holds for |x|\leq \frac{5}{3}.
x\in \begin{bmatrix}-\frac{5}{3},\frac{5}{3}\end{bmatrix}
Rewrite |x|\leq \frac{5}{3} as x\in \left[-\frac{5}{3},\frac{5}{3}\right].
Examples
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Limits
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