Solve 5k^2-6kleq0

$$5 k ^ { 2 } - 6 k \leq 0$$

Solve for k

$$k\in \begin{bmatrix}0,\frac{6}{5}\end{bmatrix}$$

Solution Steps

Factor out k.

$$k\left(5k-6\right)\leq 0$$

For the product to be ≤0, one of the values k and k-\frac{6}{5} has to be ≥0 and the other has to be ≤0. Consider the case when k\geq 0 and k-\frac{6}{5}\leq 0.

$$k\geq 0 k-\frac{6}{5}\leq 0$$

The solution satisfying both inequalities is k\in \left[0,\frac{6}{5}\right].

$$k\in \begin{bmatrix}0,\frac{6}{5}\end{bmatrix}$$

Consider the case when k\leq 0 and k-\frac{6}{5}\geq 0.

$$k-\frac{6}{5}\geq 0 k\leq 0$$

This is false for any k.

$$k\in \emptyset$$

The final solution is the union of the obtained solutions.

$$k\in \begin{bmatrix}0,\frac{6}{5}\end{bmatrix}$$