How do I do this Maths Problem? It is Absolute value. | 2a | > 4 I can do it with = signs but not >'s Please explain how thanks?

Method 1 :

|2a| > 4

|2a|² > 4²
4a² > 16
a² > 4
a² - 4 > 0
(a + 2)(a - 2) > 0
Hence, a < -2 or a > 2


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Method 2 :

Case I : When a ≥ 0, then |2a| = 2a :
|2a| > 4
2a > 4
a > 2

Case II : When a < 0, then |2a| = -2a :
|2a| > 4
-2a > 4
2a < -4
a < -2

Consider both cases, a > 2 or a < -2

| 2a | > 4 → you can extract 2 from the absolute value, because 2 is always > 0

2 * | a | > 4 → you divide by 2 both sides

| a | > 2 → the contents of an absolute value can be positive or negative.


First case: a > 0 → then the equation becomes:

+ (a) > 2

a > 2


Second case: a < 0 → then the equation becomes:

- (a) > 2

- a > 2 → you multiply both sides by (- 1), as (- 1) is negative, you change the direction

- a * (- 1) < 2 * (- 1) → you simplify

a < - 2


Then you joint the 2 cases and you can get:

x Є ] -∞ ; - 2 [ U ] 2 ; +∞ [

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