How do you solve |x – 4| + 7 = 4?

Mar 28, 2017

See the entire solution process below:

Explanation:

First, subtract $\textcolor{red}{7}$ from each side of the equation to isolate the absolute value term while keeping the equation balanced:

$\left\mid x - 4 \right\mid + 7 - \textcolor{red}{7} = 4 - \textcolor{red}{7}$

$\left\mid x - 4 \right\mid + 0 = - 3$

$\left\mid x - 4 \right\mid = - 3$

Because the absolute value function takes any term, positive or negative, and transforms it into its positive form, there are no answers for the problem because the result of the absolute value function cannot be negative.

Therefore the solution is the empty or null set or $x = \left\{\emptyset\right\}$