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Can you show the steps for solving this inequality: $$\sqrt{4x+1}+\sqrt{x+1}

Condition: $x \geq -1/4$ and $x\geq -1$.

I'm stuck here:

$$2\cdot \sqrt{(4x+1)(x+1)}

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    What have you tried so far? You can edit your question to show that, and we'll be better able to help you. – 2017-01-24
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    Please put your question *into* the text here. And perhaps a more descriptive title.. – 2017-01-24
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    both conditions together give $$x\geq -\frac{1}{4}$$ – 2017-01-24

1 Answers 1

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We have $$ x\geq -\frac{1}{4} \;, $$ and after squaring one times (all terms are non negative) we obtain $$ 4x+1+x+1+2\sqrt{x+1}\sqrt{4x+1}0 \;, $$ and this inequality gives the solution: $$ x>7.46 \ldots $$