Question
Download Solution PDFIf |x + 5| ≥ 10, then:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The Modulus Function '| |' is defined as:
\(\rm |x|=\left\{\begin{matrix}\rm \ \ \ x, &\rm x \geq 0\\ \rm -x, &\rm x<0\\\end{matrix}\right.\)
Calculation:
We have two cases:
CASE I: If x + 5 ≥ 0, then |x + 5| = x + 5.
⇒ x + 5 ≥ 10
⇒ x ≥ 5
⇒ x ∈ [5, ∞)
CASE II: If x + 5 < 0, then |x + 5| = -(x + 5).
⇒ -(x + 5) ≥ 10
⇒ -x - 5 ≥ 10
⇒ -x ≥ 15
⇒ x ≤ -15
⇒ x ∈ (-∞, -15]
∴ x ∈ (-∞, -15] ∪ [5, ∞).
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