Express the answer in interval notation..
mc002-1.jpg
[–9, –5]
(–9, 5)
mc002-2.jpg
Answers
Given : 2|x + 7|−4 ≥ 0
To Find : Express the answer in interval notation.
Solution:
2|x + 7| − 4 ≥ 0
| x | = x if x ≥ 0
= - x if x < 0
|x + 7| = (x + 7) if x + 7 ≥ 0 => x ≥ -7
2(x + 7) - 4 ≥ 0
=> 2x + 14 - 4 ≥ 0
=> 2x + 10 ≥ 0
=> 2x ≥ -10
=> x ≥ -5
x ≥ -7
Hence x ≥ -5
|x + 7| = -(x + 7) if x + 7 < 0 => x < -7
2{-(x + 7)} - 4 ≥ 0
=> -2x - 14 - 4 ≥ 0
=> -2x -18 ≥ 0
=> -18 ≥ 2x
=> -9 ≥ x
=> x ≤ - 9
x < -7
Hence x ≤ - 9
x ≤ - 9 and x ≥ -5
x ∈ (-∞ , - 9] ∪ [-5 , ∞)
x ∈ R - (-9 , - 5)
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Answer:
a
Step-by-step explanation: