Solve x+7/3-xgeq0

$$\frac{ x+7 }{ 3-x } \geq 0$$

Solve for x

$$x\in [-7,3)$$

Solution Steps

For the quotient to be ≥0, x+7 and 3-x have to be both ≤0 or both ≥0, and 3-x cannot be zero. Consider the case when x+7\leq 0 and 3-x is negative.

$$x+7\leq 0 3-x<0$$

This is false for any x.

$$x\in \emptyset$$

Consider the case when x+7\geq 0 and 3-x is positive.

$$x+7\geq 0 3-x>0$$

The solution satisfying both inequalities is x\in \left[-7,3\right).

$$x\in [-7,3)$$

The final solution is the union of the obtained solutions.

$$x\in [-7,3)$$