Question

How do you solve `|5v + 3| > - 9`?

Answer 1

There's nothing much to do here. This inequality is true for all values of `v` since `-9` is negative and absolute values are always greater than or equal to 0.

Explanation:

If, on the other hand, you were solving a problem like `|5v+3|>9`, you'd want to first say this is equivalent to the two inequalities `5v+3>9` or `5v+3<-9`. Subtracting 3 from both sides of these and then dividing both sides by the positive number 5 results in `v>6/5` or `v<-12/5`.

In other words, the solution set of the inequality `|5v+3|>9` is the union `(-infty,-12/5) cup (6/5,infty)`