First, let's simplify the left side of the inequality:
(х+2)² - (х+2)(х-5)= (x+2)(x+2) - (x+2)(x-5)= x² + 4x + 4 - (x² - 3x - 10)= x² + 4x + 4 - x² + 3x + 10= 7x + 14
Now, our inequality becomes:
7x + 14 < 14x - 7
Next, let's isolate x on one side of the inequality. We can do this by subtracting 7x from both sides:
14 < 7x - 7
Now, add 7 to both sides:
21 < 7x
Divide by 7 on both sides to solve for x:
3 < x
Therefore, the solution for the inequality (х+2)²-(х+2)(х-5) < 14х-7 is x > 3.
First, let's simplify the left side of the inequality:
(х+2)² - (х+2)(х-5)
= (x+2)(x+2) - (x+2)(x-5)
= x² + 4x + 4 - (x² - 3x - 10)
= x² + 4x + 4 - x² + 3x + 10
= 7x + 14
Now, our inequality becomes:
7x + 14 < 14x - 7
Next, let's isolate x on one side of the inequality. We can do this by subtracting 7x from both sides:
14 < 7x - 7
Now, add 7 to both sides:
21 < 7x
Divide by 7 on both sides to solve for x:
3 < x
Therefore, the solution for the inequality (х+2)²-(х+2)(х-5) < 14х-7 is x > 3.