The interval notation of the given inequalityGIven: \frac{2x-5}{2}<\frac

FobelloE

FobelloE

Answered question

2021-09-14

The interval notation of the given inequality
GIven: 2x52<5x+15

Answer & Explanation

Obiajulu

Obiajulu

Skilled2021-09-15Added 98 answers

Formula used:
The interval notation for x>a is (a,)
The interval notation for xa is [a,)
The interval notation for x<a is (,a)
The interval notation for xa is (,a]
The interval notation for a<x is (a,b)
The interval notation for axb is [a,b]
The interval notation for ax<b is [a,b)
The interval notation for a<xb is (a,b]
Calculations:
Here 2x52<5x+15
First we shall solve it using algebraic method.
Cross multiplying we get
5(2x5)<2(5x+1)
Distributing on both sides we get
5(2x)5(5)2(5x)+2(1)
10x2510x+2
Subtracting 10x from both sides
10x2510x10x+210x
252
Hence 25<2 is always true.
Hence the value of x can be any real number.
The interval notation for the value of x shall be (,)
Conclusion:
The interval notation for the value of 2x52<5x+15 shall be (,)

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