If |m + 4| = 2, what is the value of m?

Analytically

from the given equation
|m+4|=2
=> m+4= +2 or m+4= -2
m= -2 or m= -6
on using condition 1 we are getting two values of m= -2 and -6
hence statement 1 is not sufficient
now consider statement 2
its a quadratic equation
m^2+8m+12=0
=> m^2 +6m+2m+12=0
=>m(m+6)+2(m+6)=0
=>(m+2)(m+6)=0
=> m=-2 and -6
again we are getting two values
on combining equation 1 and equation 2
we are again getting m= -2 and -6
here this equation can also be solved graphically. the graph will look like a parabola opening upward and cutting the x axis at -2 and -6.
we will get the same result
Hence E

Step 1: Analyse Question Stem

It is given that |m + 4| = 2. We have to find the value of m

|x – a| represents the distance of x from a, on the number line.

Therefore, |m + 4| represents the distance of m from -4; since |m + 4| = 2, we can say,

Distance of m from -4 = 2units
Therefore, m = -2 or -6.

We now analyse the statements to find out a unique value for m.

Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE

Statement 1: m < 0.
From the question data, m = -2 or -6.

Since both values are negative, the data given in statement 1 is something that has already been established in the analysis of the question.

The data in statement 1 is insufficient to find out a unique value for m.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.

Statement 2: \(m^2\) + 8m + 12 = 0

Factorising the quadratic, \(m^2\)+ 8m + 12 = 0 can be written as,

(m + 6) (m + 2) = 0.

Therefore, m = -2 or m = -6. This is the same information furnished by the question.

The data in statement 2 is insufficient to find out a unique value for m.
Statement 2 alone is insufficient. Answer option B can be eliminated.

Step 3: Analyse Statements by combining

From statement 1: m < 0

From statement 2: m = -2 or m = -6
Since both the values of m are less than 0, there is no way of finding out the unique value of m.

The combination of statements is insufficient to find a unique value as the answer.
Statements 1 and 2 together are insufficient. Answer option C can be eliminated.

The correct answer option is E.