Question

Найдите наибольшее целое отрицательное решение неравенства 2|x+1|>x+4 Прошу, ответьте подробно...

Answer 1

1)x<-1
-2x-2>x+4
x+2x<-2-4
3x<-6
x<-2
x∈(-∞;-2)
2)x≥-1
2x+2>x+4
2x-x>4-2
x>2
x∈(2;∞)
наибольшее целое отрицательное равно -3

Answer 2

Finding the Solution to the Inequality 2|x+1| > x+4

To find the greatest negative integer solution to the inequality 2|x+1| > x+4, we can solve it step by step.

Step 1: Set up the Inequality The given inequality is 2|x+1| > x+4.

Step 2: Break it into Two Inequalities We can break the absolute value inequality into two separate inequalities: 1. x+1 > 0 and 2(x+1) > x+4 2. x+1 < 0 and -2(x+1) > x+4

Step 3: Solve the Two Inequalities Let's solve the two inequalities separately.

For x+1 > 0 and 2(x+1) > x+4: 1. When x+1 > 0, x > -1. 2. When 2(x+1) > x+4, 2x+2 > x+4, which simplifies to x > 2.

For x+1 < 0 and -2(x+1) > x+4: 1. When x+1 < 0, x < -1. 2. When -2(x+1) > x+4, -2x-2 > x+4, which simplifies to -3x > 6, and when we divide by -3, we get x < -2.

Step 4: Combine the Solutions Combining the solutions, we get -2 < x < 2.

Step 5: Find the Greatest Negative Integer Solution The greatest negative integer solution within the range -2 < x < 2 is x = -1.

Therefore, the greatest negative integer solution to the inequality 2|x+1| > x+4 is x = -1.