Question

1) |х+1|<2,5 2)|4+4х|≥3​

Answer 1

Ответ:

1)x+1<2,5

x<2,5-1

x<1,5

2)4+4x≥3

4x≥3-4

4x≥-1

x≥-1:4

x≥-0,25

вроде бы так.

извини если ошиблась

Answer 2

1. |x + 1| < 2.5:

To solve this inequality, we can break it down into two separate cases, considering both the positive and negative values within the absolute value expression.

Case 1: x + 1 > 0 In this case, the inequality simplifies to x + 1 < 2.5. Solving for x: x + 1 < 2.5 x < 2.5 - 1 x < 1.5

Case 2: x + 1 < 0 In this case, the inequality becomes -(x + 1) < 2.5. Solving for x: -(x + 1) < 2.5 x + 1 > -2.5 (multiplying by -1 and flipping the inequality sign) x > -2.5 - 1 x > -3.5

Therefore, the solution to the inequality |x + 1| < 2.5 is -3.5 < x < 1.5.

2. |4 + 4x| ≥ 3:

Similarly, we'll consider two cases based on the positive and negative values within the absolute value expression.

Case 1: 4 + 4x ≥ 3 In this case, the inequality simplifies to 4x ≥ -1. Solving for x: 4x ≥ -1 x ≥ -1/4

Case 2: -(4 + 4x) ≥ 3 Here, we multiply both sides by -1 and flip the inequality sign: 4 + 4x ≤ -3 4x ≤ -3 - 4 4x ≤ -7 x ≤ -7/4

So the solution to the inequality |4 + 4x| ≥ 3 is x ≤ -7/4 or x ≥ -1/4.

Note: Please double-check the calculations as I have done them manually.