Question

|4x+3|≥5 help me please​

Answer 1

Ответ:

|4х|≥5-3

|4х|≥2

|х|≥4:2

Х≥2

ОТВЕТ: [2:+ бесконечность)

Answer 2

To solve the inequality |4x + 3| ≥ 5, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative. Let's break it down step by step:

Case 1: 4x + 3 ≥ 5

In this case, we can remove the absolute value signs and solve the resulting linear inequality: 4x + 3 ≥ 5

Subtracting 3 from both sides: 4x ≥ 2

Dividing both sides by 4 (since the coefficient of x is 4 and it is positive): x ≥ 0.5

Case 2: -(4x + 3) ≥ 5

In this case, we need to change the sign of the inequality when removing the absolute value signs: 4x + 3 ≤ -5

Subtracting 3 from both sides: 4x ≤ -8

Dividing both sides by 4: x ≤ -2

Final Solution:

Combining the solutions from both cases, we have: x ≥ 0.5 or x ≤ -2

Therefore, the solution to the inequality |4x + 3| ≥ 5 is x ≥ 0.5 or x ≤ -2.

Please let me know if you need any further assistance!