Question 980855
You cannot know that the answer is   -11, because you have an inequality using absolute value, so you will have a set of x values; NOT just a single x value.


Think how abs(x+4) will be related to the 7 on a number line.  Either x+4 is less than 7, or -x-4 is greater than -7.  Solve for both conditions.



For x+4 POSITIVE or ZERO,
{{{x+4<7}}}
{{{x<7-4}}}
{{{highlight_green(x<3)}}}
BUT
For x+4 NEGATIVE,
{{{abs(x+4)<7}}}
{{{-x-4<7}}}---------think about this step very carefully to understand;
{{{-x-4+x<7+x}}}
{{{-4<7+x}}}
{{{-4-7<7+x-7}}}
{{{highlight_green(-11<x)}}}
{{{x>-11}}}


Put the two results together:
{{{highlight(-11<x<3)}}}.
Solutions for x are between negative eleven and positive three, EXCLUSIVE.