Question

Solve the equation. If there is more than one solution, separate them with a comma.

Answer 1

Our equation is

$7+|x+5|=4$

After some calculations:

$7+|x+5|=4\Rightarrow|x+5|=-3$

But we know that, for any number a

$|a|\ge0,$

So, this equation has no solution!

It's not possible that |x+5|<0 whatever the value of x

An alternative to the problem is:

$-7+|x+5|=4\Rightarrow|x+5|=3$

And this is a problem that can actually be solved:

There are two possible situations here:

$\begin{cases}x+5\ge0 \\ or \\ x+5<0\end{cases}$

If we choose the first option to be true, then:

$|x+5|=x+5\Rightarrow x+5=3\Rightarrow x=-2$

Or, if we choose the second option:

$|x+5|=-(x+5)\Rightarrow-(x+5)=3\Rightarrow x+5=-3\Rightarrow x=-8$