In which set do all of the values make the inequality 2x-1 <10 true?
2 answers:
Answer:
The set of values which makes the given inequality true for all the values
Step-by-step explanation:
The given inequality is : 2x - 1 < 10
We need to find all the values of x for which the given inequality is true.
So, in order to do so, we need to solve the inequality for x.
Now, 2x - 1 < 10
Adding 1 on both the sides.
⇒ 2x - 1 + 1 < 10 + 1
⇒ 2x < 11
Dividing each term on both the sides by 2
Therefore, The set of values which makes the given inequality true for all the values :
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The first term will be 3 and the sum of the first 9 terms will be 81.
<h3>What is Arithmetic progression?</h3>The difference between every two successive terms in a sequence is the same this is known as an arithmetic progression (AP).
The arithmetic progression has wider use in mathematics for example sum of natural numbers.
Natural number = 1,2,3,4,5,6,7,8...
Given,
Six terms as 10.5
So,
a₆ = 10.5
Common difference(d) = 1.5
The nth term of an AP is given by
= a + (n-1)d
So,
a₆ = a + (6-1)d
10.5 = a + 5(1.5)
a = 3
Now,
The Sum of n terms is given by
S = n/2[2a + (n-1)d]
S = 9/2[6 + 8(1.5)]
S = 81
Hence the first term will be 3 and the sum of 9 terms will be 81.
For more about Arithmetic progression
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