Solve for x
x\in \begin{bmatrix}-\frac{\sqrt{7}}{7},\frac{\sqrt{7}}{7}\end{bmatrix}
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-1+7x^{2}\leq 0
Multiply the inequality by -1 to make the coefficient of the highest power in 1-7x^{2} positive. Since -1 is negative, the inequality direction is changed.
x^{2}\leq \frac{1}{7}
Add \frac{1}{7} to both sides.
x^{2}\leq \left(\frac{\sqrt{7}}{7}\right)^{2}
Calculate the square root of \frac{1}{7} and get \frac{\sqrt{7}}{7}. Rewrite \frac{1}{7} as \left(\frac{\sqrt{7}}{7}\right)^{2}.
|x|\leq \frac{\sqrt{7}}{7}
Inequality holds for |x|\leq \frac{\sqrt{7}}{7}.
x\in \begin{bmatrix}-\frac{\sqrt{7}}{7},\frac{\sqrt{7}}{7}\end{bmatrix}
Rewrite |x|\leq \frac{\sqrt{7}}{7} as x\in \left[-\frac{\sqrt{7}}{7},\frac{\sqrt{7}}{7}\right].
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