Solve for x
x\in (-\infty,-1]\cup [0,\infty)
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3x^{2}+3x\geq 0
Multiply the inequality by -1 to make the coefficient of the highest power in -3x^{2}-3x positive. Since -1 is negative, the inequality direction is changed.
3x\left(x+1\right)\geq 0
Factor out x.
x+1\leq 0 x\leq 0
For the product to be ≥0, x+1 and x have to be both ≤0 or both ≥0. Consider the case when x+1 and x are both ≤0.
x\leq -1
The solution satisfying both inequalities is x\leq -1.
x\geq 0 x+1\geq 0
Consider the case when x+1 and x are both ≥0.
x\geq 0
The solution satisfying both inequalities is x\geq 0.
x\leq -1\text{; }x\geq 0
The final solution is the union of the obtained solutions.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}