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Directions: Select a single answer choice.
Q. How many integers are in the solution set of the inequality x2 − 10 < />
- a)Two
- b)Five
- c)Six
- d)Seven
- e)Ten
Correct answer is option 'D'. Can you explain this answer?
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Directions: Select a single answer choice.Q. How many integers are in...
The inequality x2 − 10 < 0="" is="" equivalent="" to="" />2 < 10.="" by="" inspection,="" the="" positive="" integers="" that="" satisfy="" this="" inequality="" are="" 1,="" 2,="" and="" 3.="" note="" that="" 0="" and="" the="" negative="" integers="" −1,="" −2="" ,="" and="" −3="" also="" satisfy="" the="" inequality,="" and="" there="" are="" no="" other="" integer="" solutions.="" so="" there="" are="" seven="" integers="" in="" the="" solution="" set:="" −3,="" −2,="" −1,="" 0,="" 1,="" 2,="" and="" 3.="" thus="" the="" correct="" answer="" is="" choice="" d.="" 10.="" by="" inspection,="" the="" positive="" integers="" that="" satisfy="" this="" inequality="" are="" 1,="" 2,="" and="" 3.="" note="" that="" 0="" and="" the="" negative="" integers="" −1,="" −2="" ,="" and="" −3="" also="" satisfy="" the="" inequality,="" and="" there="" are="" no="" other="" integer="" solutions.="" so="" there="" are="" seven="" integers="" in="" the="" solution="" set:="" −3,="" −2,="" −1,="" 0,="" 1,="" 2,="" and="" 3.="" thus="" the="" correct="" answer="" is="" choice="" />
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Directions: Select a single answer choice.Q. How many integers are in...
Understanding the Inequality:
- The inequality given is x^2 - 10.
- To find the solution set, we need to determine the values of x that satisfy this inequality.
Finding the Solution Set:
- To solve x^2 - 10, we set it greater than or equal to 0: x^2 - 10 ≥ 0.
- This simplifies to x^2 ≥ 10.
- Taking the square root of both sides gives us x ≥ √10 or x ≤ -√10.
Determining the Integers:
- The square root of 10 is approximately 3.16, so we have integers ranging from -3 to 3 that satisfy the inequality.
- Therefore, the integers in the solution set are -3, -2, -1, 0, 1, 2, and 3.
Counting the Integers:
- There are 7 integers in the solution set of the inequality x^2 - 10.
Therefore, the correct answer is option D) Seven, as there are 7 integers that satisfy the given inequality.
- The inequality given is x^2 - 10.
- To find the solution set, we need to determine the values of x that satisfy this inequality.
Finding the Solution Set:
- To solve x^2 - 10, we set it greater than or equal to 0: x^2 - 10 ≥ 0.
- This simplifies to x^2 ≥ 10.
- Taking the square root of both sides gives us x ≥ √10 or x ≤ -√10.
Determining the Integers:
- The square root of 10 is approximately 3.16, so we have integers ranging from -3 to 3 that satisfy the inequality.
- Therefore, the integers in the solution set are -3, -2, -1, 0, 1, 2, and 3.
Counting the Integers:
- There are 7 integers in the solution set of the inequality x^2 - 10.
Therefore, the correct answer is option D) Seven, as there are 7 integers that satisfy the given inequality.
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Directions: Select a single answer choice.Q. How many integers are in the solution set of the inequality x2 − 10 a)Twob)Fivec)Sixd)Sevene)TenCorrect answer is option 'D'. Can you explain this answer?
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