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## 7+/x+4/=12

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.

Generally

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 )

So,

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.)