Solve X^2-2Xleq0

$$X ^ { 2 } - 2 X \leq 0$$

Solve for X

$$X\in \begin{bmatrix}0,2\end{bmatrix}$$

Solution Steps

Factor out X.

$$X\left(X-2\right)\leq 0$$

For the product to be ≤0, one of the values X and X-2 has to be ≥0 and the other has to be ≤0. Consider the case when X\geq 0 and X-2\leq 0.

$$X\geq 0 X-2\leq 0$$

The solution satisfying both inequalities is X\in \left[0,2\right].

$$X\in \begin{bmatrix}0,2\end{bmatrix}$$

Consider the case when X\leq 0 and X-2\geq 0.

$$X-2\geq 0 X\leq 0$$

This is false for any X.

$$X\in \emptyset$$

The final solution is the union of the obtained solutions.

$$X\in \begin{bmatrix}0,2\end{bmatrix}$$