Question

|x-3|>1,8 решить неравенство

Answer 1

|х-3|>1,8
|х-3|<-1,8
{х>1,2
{х<4,8

Answer 2

To solve the inequality |x - 3| > 1, we need to consider two cases since the absolute value can be positive or negative:

Case 1: (x - 3) > 1 In this case, we remove the absolute value by simply dropping it since it is positive. x - 3 > 1 Add 3 to both sides: x > 1 + 3 x > 4

Case 2: -(x - 3) > 1 In this case, we remove the absolute value by dropping it and reversing the inequality sign since we are multiplying by -1, which reverses the inequality direction. -(x - 3) > 1 -x + 3 > 1 Subtract 3 from both sides: -x > 1 - 3 -x > -2 Now, multiply both sides by -1 (remember to reverse the inequality sign): x < 2

So, the solutions to the inequality |x - 3| > 1 are x < 2 and x > 4. In interval notation, the solution is (-∞, 2) ∪ (4, ∞).