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Find the solution set for x:
4 < −x + 7 < 15
  • a)
    x ∈ (−8, 3)
  • b)
    x ∈ (3, 8)
  • c)
    x ∈ (−∞, 3) ∪ (8, ∞)
  • d)
    x ∈ (−3, 8)
  • e)
    x ∈ (−∞, −3) ∪ (8, ∞)
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Find the solution set for x:4 < −x + 7 < 15a)x ∈ (&mi...
4 < −x + 7 < 15 
Subtract 7:
4 − 7 < −x + 7 − 7 < 15 − 7
−3 < −x < 8
Divide by -1. Don't forget to switch the direction of the inequality signs since we're dividing by a negative number:
−3 ⋅ (−1) > −x ⋅ (−1) > 8 ⋅ (−1)
Simplify:
3 > x > −8 or in interval form, (−8, 3).
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Find the solution set for x:4 < −x + 7 < 15a)x ∈ (−8, 3)b)x ∈ (3, 8)c)x ∈ (−∞, 3) ∪ (8, ∞)d)x ∈ (−3, 8)e)x ∈ (−∞, −3) ∪ (8, ∞)Correct answer is option 'A'. Can you explain this answer?
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