Solve 5x-x^2/4geq0

$$\frac { 5 x - x ^ { 2 } } { 4 } \geq 0$$

Solve for x

$$x\in \begin{bmatrix}0,5\end{bmatrix}$$

Solution Steps

Multiply both sides by 4. Since 4 is positive, the inequality direction remains the same. Anything times zero gives zero.

$$5x-x^{2}\geq 0$$

Multiply the inequality by -1 to make the coefficient of the highest power in 5x-x^{2} positive. Since -1 is negative, the inequality direction is changed.

$$-5x+x^{2}\leq 0$$

Factor out x.

$$x\left(x-5\right)\leq 0$$

For the product to be ≤0, one of the values x and x-5 has to be ≥0 and the other has to be ≤0. Consider the case when x\geq 0 and x-5\leq 0.

$$x\geq 0 x-5\leq 0$$

The solution satisfying both inequalities is x\in \left[0,5\right].

$$x\in \begin{bmatrix}0,5\end{bmatrix}$$

Consider the case when x\leq 0 and x-5\geq 0.

$$x-5\geq 0 x\leq 0$$

This is false for any x.

$$x\in \emptyset$$

The final solution is the union of the obtained solutions.

$$x\in \begin{bmatrix}0,5\end{bmatrix}$$