Solve 4x^2-xleq0

$$4 x ^ { 2 } - x \leq 0$$

Solve for x

$$x\in \begin{bmatrix}0,\frac{1}{4}\end{bmatrix}$$

Solution Steps

Factor out x.

$$x\left(4x-1\right)\leq 0$$

For the product to be ≤0, one of the values x and x-\frac{1}{4} has to be ≥0 and the other has to be ≤0. Consider the case when x\geq 0 and x-\frac{1}{4}\leq 0.

$$x\geq 0 x-\frac{1}{4}\leq 0$$

The solution satisfying both inequalities is x\in \left[0,\frac{1}{4}\right].

$$x\in \begin{bmatrix}0,\frac{1}{4}\end{bmatrix}$$

Consider the case when x\leq 0 and x-\frac{1}{4}\geq 0.

$$x-\frac{1}{4}\geq 0 x\leq 0$$

This is false for any x.

$$x\in \emptyset$$

The final solution is the union of the obtained solutions.

$$x\in \begin{bmatrix}0,\frac{1}{4}\end{bmatrix}$$