Question

solve |x+2| >5
do not post irrelevant answer​

Answer 1

Answer :

x € (-∞,-7)U(3,∞)

Note :

★ Modules function / Absolute value :

• Absolute value of any real number x is denoted by |x| .

• f(x) = |x|

Modules function is defined as ;

• f(x) = x , if x ≥ 0

= -x , if x < 0

• f(x) = max {x , -x}

★ If |x| = a , then x = ± a

★ If |x| < a , then -a < x < a OR x € (a,-a) .

★ If |x| ≤ a , then -a ≤ x ≤ a OR x € [a,-a] .

★ If |x| > a , then x < -a or x > a

OR x € (-∞,-a)U(a,∞) .

★ If |x| ≥ a , then x ≤ -a or x ≥ a

OR x € (-∞,-a]U[a,∞) .

Solution :

• Given : |x + 2| > 5
• To find : x = ?

We have ,

=> |x + 2| > 5

=> x + 2 < -5 or x + 2 > 5

=> x < -5 - 2 or x > 5 - 2

=> x < -7 or x > 3

=> x € (-∞,-7) or x € (3,∞)

=> x € (-∞,-7)U(3,∞)

Hence ,

x € (-∞,-7)U(3,∞)