How do you solve |6n - 3| + 11= 4?

Jul 7, 2017

To solve the equation, isolate the variable n.
However, as you cannot simplify the equation anymore, you will find that it does not have any possible solutions.

Explanation:

$| 6 n - 3 | + 11 = 4$
$| 6 n - 3 | = - 7$ ---> NO SOLUTION.

Why isn't there a solution? Here's why...

With n = a certain number, the absolute value of $6 n - 3$ basically changes the resulting value of the expression (positive or negative, regardless) to a positive number.
Example: Let's use $n = 0$. --> $| 6 \left(0\right) - 3 |$ --> $| 0 - 3 |$ --> $| - 3 |$ = 3.

Because it is impossible to get a negative number ($- 7$, in this case) with an absolute value ( $| 6 n - 3 |$ ), no values of n are possible.

I hope this helps a lot! :)