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