Question

2^(x-1)-3*2^x+2>-23 помогите пожалуйста

Answer 1

-4дробьх больше -23
Нет

Answer 2

Solving the Inequality 2^(x-1) - 3*2^x + 2 > -23

To solve the inequality 2^(x-1) - 3*2^x + 2 > -23, we can follow these steps:

1. Simplify the Inequality: - Rewrite the inequality in a simpler form to make it easier to solve.

2. Solve for x: - Use algebraic techniques to solve for the variable x.

Simplifying the Inequality

The given inequality is: 2^(x-1) - 3*2^x + 2 > -23

Solving for x

To solve the inequality, we can start by simplifying the terms involving 2^x and 2^(x-1). Then, we can proceed to isolate x.

First, let's simplify the terms: 2^(x-1) can be rewritten as 2^x / 2 So, the inequality becomes: 2^x / 2 - 3*2^x + 2 > -23

Now, we can combine the terms involving 2^x: 2^x / 2 - 3*2^x can be rewritten as (1/2)*2^x - 3*2^x = (1/2 - 3)*2^x = (-5/2)*2^x

So, the inequality becomes: (-5/2)*2^x + 2 > -23

Next, we can isolate the term involving 2^x: (-5/2)*2^x > -23 - 2 (-5/2)*2^x > -25

Now, we can solve for x: 2^x > -25 * (-2/5) 2^x > 50

Taking the logarithm of both sides: x*log(2) > log(50) x > log(50) / log(2)

Using a calculator, we find: x > 5.64385618977

Therefore, the solution to the inequality 2^(x-1) - 3*2^x + 2 > -23 is x > 5.64385618977.