Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
To determine the integer values of [tex]\( n \)[/tex] that satisfy the inequality [tex]\( -15 < 3n \leq 6 \)[/tex], we need to follow these steps:
1. Divide the entire inequality by 3 to isolate [tex]\( n \)[/tex]:
[tex]\[ -15 < 3n \leq 6 \][/tex]
Dividing everything by 3, we get:
[tex]\[ \frac{-15}{3} < \frac{3n}{3} \leq \frac{6}{3} \][/tex]
Simplifying this, we have:
[tex]\[ -5 < n \leq 2 \][/tex]
2. Find the integer values of [tex]\( n \)[/tex] within this range:
We need to find all integers [tex]\( n \)[/tex] that are greater than [tex]\(-5\)[/tex] and less than or equal to [tex]\( 2 \)[/tex]. These are the values of [tex]\( n \)[/tex] that satisfy the inequality:
[tex]\[ -5 < n \leq 2 \][/tex]
Listing the integers within this range, we start from the smallest integer greater than [tex]\(-5\)[/tex] and go up to [tex]\(2\)[/tex]:
[tex]\[ -4, -3, -2, -1, 0, 1, 2 \][/tex]
Therefore, the integer values of [tex]\( n \)[/tex] that satisfy the inequality [tex]\( -15 < 3n \leq 6 \)[/tex] are:
[tex]\[ n \in \{-4, -3, -2, -1, 0, 1, 2\} \][/tex]
1. Divide the entire inequality by 3 to isolate [tex]\( n \)[/tex]:
[tex]\[ -15 < 3n \leq 6 \][/tex]
Dividing everything by 3, we get:
[tex]\[ \frac{-15}{3} < \frac{3n}{3} \leq \frac{6}{3} \][/tex]
Simplifying this, we have:
[tex]\[ -5 < n \leq 2 \][/tex]
2. Find the integer values of [tex]\( n \)[/tex] within this range:
We need to find all integers [tex]\( n \)[/tex] that are greater than [tex]\(-5\)[/tex] and less than or equal to [tex]\( 2 \)[/tex]. These are the values of [tex]\( n \)[/tex] that satisfy the inequality:
[tex]\[ -5 < n \leq 2 \][/tex]
Listing the integers within this range, we start from the smallest integer greater than [tex]\(-5\)[/tex] and go up to [tex]\(2\)[/tex]:
[tex]\[ -4, -3, -2, -1, 0, 1, 2 \][/tex]
Therefore, the integer values of [tex]\( n \)[/tex] that satisfy the inequality [tex]\( -15 < 3n \leq 6 \)[/tex] are:
[tex]\[ n \in \{-4, -3, -2, -1, 0, 1, 2\} \][/tex]
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.