about equation absolute-value
if x+4 is positive that means that |x+4|=x+4 we can simplify the equation and write
7+x+4=12 so x=1 and if x+4 is negative that means that |x+4|= -x-4 and so we can simplify he
equation and write 7-x-4=12 so x= -9.
It seems the given equation is 7 + l x + 4 l = 12.
Absolute value has to be divided into two conditions. such as when it is bigger than and equal to zero and when it is smaller than zero.
l a l = a ( when a ≥0 )
= -a ( when a <0 ) this is tedious work but every time you have to consider like this.
Now, l x + 4 l = x + 4 ( when x + 4 ≥ 0, this is the same as x ≥ -4 )
l x + 4 l = -(x + 4) = -x -4 ( when x + 4 < 0, this is the same as x < -4 )
1) when x ≥ -4 , 7 + x + 4 = 12
x = 1 ( check this x value with the condition of given x range, which is x is bigger and equal to -4, this condition is satisfied by the x = 1. so x = 1 is an answer.)
2) when x < -4, 7 - x - 4 = 12
x = -9 ( check this x value with the given x range, which is x is smaller than -4, x = -9 satisfies the given condition. So x = -9 is an another answer.)
Hope this help you.