What is 2^{x+2}-2^{x+1}+2^{x-1}-2^{x-2}<= 9 ?

The solution to 2^{x+2}-2^{x+1}+2^{x-1}-2^{x-2}<= 9 is x<= 2

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2^{x+2}-2^{x+1}+2^{x-1}-2^{x-2}<= 9

2^{x + 2} - 2^{x + 1} + 2^{x - 1} - 2^{x - 2} \leq 9

x \leq 2

Interval Notation

(- \infty, 2]

Solution steps

2^{x + 2} - 2^{x + 1} + 2^{x - 1} - 2^{x - 2} \leq 9

Apply exponent rules

2^{x} \cdot 2^{2} - 2^{x} \cdot 2 + \frac{2 ^{x}}{2} - \frac{2 ^{x}}{2 ^{2}} \leq 9

Factor

2^{x} \cdot 2^{2} - 2^{x} \cdot 2 + \frac{2 ^{x}}{2} - \frac{2 ^{x}}{2 ^{2}} : 9 \cdot 2^{x - 2}

9 \cdot 2^{x - 2} \leq 9

Divide both sides by

9

\frac{9 \cdot 2 ^{x - 2}}{9} \leq \frac{9}{9}

Simplify

2^{x - 2} \leq 1

Apply exponent rules

x - 2 \leq 0

Move

2

to the right side

x \leq 2

c^{2} - 12 c + 35

- 5

3 k - 4 = 5 + 2 (k - 3)

\frac{n ^{2} - 4}{2} = 16

2 u + 4 > 14 or 4 u + 2 > - 10

What is 2^{x+2}-2^{x+1}+2^{x-1}-2^{x-2}<= 9 ?
The solution to 2^{x+2}-2^{x+1}+2^{x-1}-2^{x-2}<= 9 is x<= 2