1. ## Inequalities question

22x − 2(2x) ≤ −1

What methods can I use to solve this??

2. ## Re: Inequalities question

Originally Posted by Aviator_13
22x − 2(2x) ≤ −1

What methods can I use to solve this??
$\noindent \textbf{Hint.} If you substitute u = 2^{x}, then you get a quadratic inequation to solve in u (noting that u > 0 also because u = 2^{x}). So you can do the question if you've learnt how to solve quadratic inequations.$

3. ## Re: Inequalities question

This is what I got.

$2^{2x} -2(2^x) \leq -1$

$Let u= 2^x$

$∴ Using substitution...$

$u^2 - 2u \leq -1$

$u^2 -2u + 1 \leq 0$

$(u-1)^2 \leq 0$

$When you graph the above inequality, you'll see that the parabola has a value equal to 0 at u = 1. It's never less than 0 though. Therefore, all we need to do is just substitute u = 1 back into u = 2^x$

$2^x = 1$

$x = \log_{2}1$

I hope that's correct!

4. ## Re: Inequalities question

Thank you!!

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