Question

Which inequality is true?

Answer 1

`\boxed{\sf Option \ C \ is \ correct .}`

Explanation:

We need to tell which of the given inequality is true . The given inequalities are ,

`\sf A)\pi + 8 <11\\\\\sf B) (\pi)/(8) > 2 \\\\\sf C) 3\pi > 9 \\\\\sf D) 2\pi - 1 < 5`

Let's check the options one by one .

Option A :-

`\sf\longrightarrow \pi + 8 < 11`

Subtract 8 to both sides ,

`\sf\longrightarrow \pi < 11 - 8`

Simplify ,

`\sf\longrightarrow \pi < 3`

We know the approximate value of pi 3.14 . But the inequality says pi is less than 3 . Therefore the given inequality is incorrect .

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Option B :-

`\sf\longrightarrow (\pi)/(2) > 2`

Multiply both sides by 2 ,

`\sf\longrightarrow \pi > 4`

We know the approximate value of pi 3.14 . But the inequality says pi is more than 4 . Therefore the given inequality is incorrect .

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Option C :-

`\sf\longrightarrow 3 \pi > 9`

Divide both sides by 3 ,

`\sf\longrightarrow \pi < 9/3`

Simplify ,

`\sf\longrightarrow \pi > 3`

We know the approximate value of pi 3.14 .And the inequality says pi is more than 3 . Therefore the given inequality is correct .

Option C is correct .