Question

PLEASE SOLVE AND CHECK. SHOW COMPLETE SOLUTION

Answer 1

4/3
`\geq` x

Explanation:

`(√(x+4))^ {2} \geq (2√(x))^(2)\\`

x + 4
`\geq` 4x

4
`\geq` 4x - x

4
`\geq` 3x

4/3
`\geq` x

Answer 2

`√(x + 4) \geqslant 2 √(x)`

• Square both sides.

`= > ( √(x + 4)) ^(2) = (2 √(x) ) ^(2) \\`

• In the LHS, square and square root gets cancelled out. In the RHS, do the square.

`= > x + 4 \geqslant {2}^(2) x \\ = > x + 4 \geqslant 4x`

• Transpose x to the RHS.

`= > 4 \geqslant 4x - x \\ = > 3x \leqslant 4`

• Now, divide both sides by 3.

`= > (3x)/(3) \leqslant (4)/(3) \\ = > x \leqslant (4)/(3)`

Answer:

`x \leqslant (4)/(3)`

Hope you could understand.

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