# Homework Help: Exponential inequations.

1. Oct 2, 2008

### enibaraliu

1. The problem statement, all variables and given/known data
1) 5x+4-5x-1<24
2) 2x+2-1>=22x+3
3) 21-x-2x+1/2x-1<0

2. Relevant equations
At the 2nd I do like this:
2x+2-22x>=4 devide by 2
2x+1-22x-1>=2
x+1-2x+1>=1
-x>=-1 devide by (-1)
x=<1
but when i put 0 in x the inequation is incorrect, what I have mistake, please tell me.
If you can halp me in anothers inequations, thanks a lot.

3. The attempt at a solution

2. Oct 2, 2008

### enibaraliu

Please can you help for this?

3. Oct 2, 2008

### enibaraliu

4. Oct 2, 2008

Your simplifications with the exponents aren't correct. Try this:

\begin{align*} 2^{x+2} - 2^{2x} & \ge 4\\ 2^x \cdot 2^2 - 2^{2x} & \ge 4\\ 4\cdot 2^x - 2^{2x} -4 & \ge 0\\ 2^{2x} - 4\cdot 2^x + 4 & \le 0 \end{align*}

Now, for ease of reading, let

$$u = 2^x \Rightarrow u^2 = 2^{2x}$$

so the inequality is now

$$u^2 - 4u + 4 & \le 0$$