Question

(2x-1)^2+5x<(1+2x)(2x-1)​

Answer 1

Надеюсь понятно, если нет, то спрашивай

Answer 2

To solve the inequality, let's first simplify the expressions on both sides and then find the solution:

Given inequality: (2x-1)^2 + 5x < (1 + 2x)(2x-1)

Step 1: Simplify both sides of the inequality

Expand the squared term on the left side: (2x-1)^2 = (2x-1)(2x-1) = 4x^2 - 4x + 1

Expand the right side: (1 + 2x)(2x-1) = 2x(2x-1) + (2x-1) = 4x^2 - 2x + 2x - 1 = 4x^2 - 1

So, the inequality becomes: 4x^2 - 4x + 1 + 5x < 4x^2 - 1

Step 2: Combine like terms

4x^2 - 4x + 5x + 1 < 4x^2 - 1

Step 3: Simplify further

4x^2 + x + 1 < 4x^2 - 1

Step 4: Move all terms to one side of the inequality

4x^2 - 4x^2 + x + 1 < 4x^2 - 4x^2 - 1

Simplify:

x + 1 < -1

Step 5: Isolate x on one side

x < -1 - 1

x < -2

The solution to the inequality is x < -2.