Question

How do you solve the equation `abs(7x-1)+2=0`?

Answer 1

No solution

Explanation:

The `|cdot|` notation refers to the absolute value, or changing whatever is inside to its distance from `0` on a graph. For example, `|3|=3` and `|-3|=3`. The result is always positive.

Considering the equation, we can slightly rearrange it to
`|7x-1|+2=0`
`|7x-1|=-2`

Now, no matter what `x` is (real, imaginary, complex, etc.), the absolute value of `7x-1` will always be positive and can never be equal to `-2`.

Thus, there is no solution to the equation.

Now, if the equation was instead
`|7x-1|=2`
we would have to consider the case that `7x-1=2` and the case that `7x-1=-2` to arrive at the different possible solutions.