Solve xleq(400-x)x

$$x \leq ( 400 - x ) x$$

Solve for x

$$x\in \begin{bmatrix}0,399\end{bmatrix}$$

Solution Steps

Use the distributive property to multiply 400-x by x.

$$x\leq 400x-x^{2}$$

Subtract 400x from both sides.

$$x-400x\leq -x^{2}$$

Combine x and -400x to get -399x.

$$-399x\leq -x^{2}$$

Add x^{2} to both sides.

$$-399x+x^{2}\leq 0$$

Factor out x.

$$x\left(x-399\right)\leq 0$$

For the product to be ≤0, one of the values x and x-399 has to be ≥0 and the other has to be ≤0. Consider the case when x\geq 0 and x-399\leq 0.

$$x\geq 0 x-399\leq 0$$

The solution satisfying both inequalities is x\in \left[0,399\right].

$$x\in \begin{bmatrix}0,399\end{bmatrix}$$

Consider the case when x\leq 0 and x-399\geq 0.

$$x-399\geq 0 x\leq 0$$

This is false for any x.

$$x\in \emptyset$$

The final solution is the union of the obtained solutions.

$$x\in \begin{bmatrix}0,399\end{bmatrix}$$