Solve 1+1/ageq0

$$1 + \frac { 1 } { a } \geq 0$$

Solve for a

$$a\in (-\infty,-1]\cup (0,\infty)$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{a}{a}.

$$\frac{a}{a}+\frac{1}{a}\geq 0$$

Since \frac{a}{a} and \frac{1}{a} have the same denominator, add them by adding their numerators.

$$\frac{a+1}{a}\geq 0$$

For the quotient to be ≥0, a+1 and a have to be both ≤0 or both ≥0, and a cannot be zero. Consider the case when a+1\leq 0 and a is negative.

$$a+1\leq 0 a<0$$

The solution satisfying both inequalities is a\leq -1.

$$a\leq -1$$

Consider the case when a+1\geq 0 and a is positive.

$$a+1\geq 0 a>0$$

The solution satisfying both inequalities is a>0.

$$a>0$$

The final solution is the union of the obtained solutions.

$$a\leq -1\text{; }a>0$$