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Question

Answers

(a) 3 < x < 11

(b) 9 < x < 11

(c) 9 < x < 121

(d) x < 3 or x < 11

(e) x < 9 or x < 121

Answer
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Given that the positive square root of x lies between 3 and 11. We need to find the inequality that represents all possible values of x.

According to the problem, we have got the inequality $3<\sqrt{x}<11$.

Since 3 and 11 are greater than zero and the signs of the inequality doesn’t change on squaring the inequality.

So, we square each term of inequality $3<\sqrt{x}<11$.

So, we have got the inequality ${{3}^{2}}<{{\left( \sqrt{x} \right)}^{2}}<{{11}^{2}}$ ---(1).

We know that ${{\left( \sqrt{x} \right)}^{2}}=x$ and we use this result in equation (1).

We have got the inequality $9 < x < 121$.

We have found the inequality that represents all possible values of x as $9 < x < 121$.

∴ The inequality that represents all possible values of x is $9 < x < 121$.