Question

`(1)/(2 √(x) ) \geqslant (1)/(16)`
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Answer 1

`0\le x\le 64`

Explanation:

`(1)/(2√(x) ) \geq (1)/(16)`

Using substitution

`√(x) = t`

`(1)/(2t) \geq (1)/(16)`

Multiply both sides by 2

`(1)/(t) \geq (1)/(8)`

Multiply both sides by
`t`. We can do it because
`t > 0`

`1 \geq (t)/(8)`

Multiply both sides by 8

`8 \geq t`

As
`t=√(x)`

`8 \geq √(x)`

So

`x\le 64\cap x\ge 0`

`0\le x\le 64`