Solve for x
x\in \begin{bmatrix}-3,3\end{bmatrix}
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-2x-x^{2}+15+2x-6\geq 0
Use the distributive property to multiply x+5 by 3-x and combine like terms.
-x^{2}+15-6\geq 0
Combine -2x and 2x to get 0.
-x^{2}+9\geq 0
Subtract 6 from 15 to get 9.
x^{2}-9\leq 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}\leq 9
Add 9 to both sides.
x^{2}\leq 3^{2}
Calculate the square root of 9 and get 3. Rewrite 9 as 3^{2}.
|x|\leq 3
Inequality holds for |x|\leq 3.
x\in \begin{bmatrix}-3,3\end{bmatrix}
Rewrite |x|\leq 3 as x\in \left[-3,3\right].
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}