Question

32.30. 1) (3x - 1)²-7<(9x + 2)x+ 2; 2) 2x(8x + 3) +1> (5-4x)2-1;

Answer 1

2 ю не поняла!!!!!!!!!!!!

Answer 2

Let's solve each inequality step by step:

1. (3x - 1)² - 7 < (9x + 2)x + 2

Expanding the squared term: (9x² - 6x + 1) - 7 < (9x + 2)x + 2

Simplifying the right side: 9x² - 6x - 6 < 9x² + 2x + 2

Combining like terms: -6x - 6 < 2x + 2

Moving all terms to one side: -6x - 2x < 2 + 6

-8x < 8

Dividing both sides by -8 and reversing the inequality sign (since we are dividing by a negative number): x > -1

Therefore, the solution for the inequality (3x - 1)² - 7 < (9x + 2)x + 2 is x > -1.

2. 2x(8x + 3) + 1 > (5 - 4x)² - 1

Expanding the left side: 16x² + 6x + 1 > (5 - 4x)² - 1

Expanding the squared term on the right side: 16x² + 6x + 1 > (25 - 20x + 16x²) - 1

Simplifying the right side: 16x² + 6x + 1 > 25 - 20x + 16x² - 1

Combining like terms: 16x² - 16x² + 6x + 20x > 25 - 1 - 1

Simplifying further: 26x > 23

Dividing both sides by 26: x > 23/26

Therefore, the solution for the inequality 2x(8x + 3) + 1 > (5 - 4x)² - 1 is x > 23/26.