Hi carrerswitch,

Let me explain the concept with a different example. When we need to find the distance between two numbers, let's say 5 and 2, we write 5 - 2 = 3.

In the same way when we need to find the distance between 5 and -2 we write 5 - (-2) = 5 + 2 = 7.

Now we know that |x| = Distance of x from 0 i.e. | x - 0|.

So, distance of x from a can be written as | x - a|. In the same manner distance of -a from x can be written as | x - (-a)| = |x + a|

Hope this helps

Regards
Harsh
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Official Explanation

Correct Answer: E

The question asks us to maximize the value of |x+a|

|x+a| measures the distance of x from the point –a on the number line.

Out of the five points, the point that is the most distant from –a is T.


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Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
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For maximum Absolute value of (x + a)

1) Sign of both x and a must be same i.e. either both must be positive or both must be negative i.e. both x and a must be on the same side on Number Line

2) We need to pick the the highest value of a or x and both a and x must be farthest from Zero so that their absolute values are maximum.

The figure says it all that both conditions are satisfied when the value of x is taken at Point T (Farthest from Zero) and we can observe that a is positive (being towards the right of Zero on Number Line)

Answer: Option E
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