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

Apr 16, 2018

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
$| 7 x - 1 | + 2 = 0$
$| 7 x - 1 | = - 2$

Now, no matter what $x$ is (real, imaginary, complex, etc.), the absolute value of $7 x - 1$ 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
$| 7 x - 1 | = 2$
we would have to consider the case that $7 x - 1 = 2$ and the case that $7 x - 1 = - 2$ to arrive at the different possible solutions.