Question

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

Answer 1

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:

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

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

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

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

I hope this helps a lot! :)