Question

|х-1|+|х+2|-|х-3|+4 помогите пожалуста срочно!!!!!! за полное обяснение 100 балов

Answer 1

Ответ:

|x-1| это ровно к 0,01 и т.д

Answer 2

Solving the Absolute Value Equation

To solve the absolute value equation |x-1| + |x+2| - |x-3| + 4, we'll need to consider different cases based on the values of x that make the expressions inside the absolute value bars positive or negative.

1. Case 1: x < 1 When x < 1, the expressions inside the absolute value bars become negative.

2. Case 2: 1 ≤ x < -2 When 1 ≤ x < -2, the expressions inside the absolute value bars become positive, negative, and positive, respectively.

3. Case 3: -2 ≤ x < 3 When -2 ≤ x < 3, the expressions inside the absolute value bars become positive, positive, and positive, respectively.

4. Case 4: x ≥ 3 When x ≥ 3, the expressions inside the absolute value bars become positive.

Solution Steps

Let's solve the equation step by step for each case:

1. Case 1: x < 1 - For x < 1, the equation becomes: -(x-1) - (x+2) - (x-3) + 4 - Simplifying, we get: -x + 1 - x - 2 - x + 3 + 4 - Combining like terms, we get: -3x + 6 - So, for x < 1, the equation simplifies to -3x + 6.

2. Case 2: 1 ≤ x < -2 - For 1 ≤ x < -2, the equation becomes: (x-1) - (x+2) - (x-3) + 4 - Simplifying, we get: x - 1 - x - 2 - x + 3 + 4 - Combining like terms, we get: -3 - So, for 1 ≤ x < -2, the equation simplifies to -3.

3. Case 3: -2 ≤ x < 3 - For -2 ≤ x < 3, the equation becomes: (x-1) + (x+2) - (x-3) + 4 - Simplifying, we get: x - 1 + x + 2 - x + 3 + 4 - Combining like terms, we get: 2x + 8 - So, for -2 ≤ x < 3, the equation simplifies to 2x + 8.

4. Case 4: x ≥ 3 - For x ≥ 3, the equation becomes: (x-1) + (x+2) + (x-3) + 4 - Simplifying, we get: x - 1 + x + 2 + x - 3 + 4 - Combining like terms, we get: 3x + 2 - So, for x ≥ 3, the equation simplifies to 3x + 2.

Conclusion

In conclusion, the absolute value equation |x-1| + |x+2| - |x-3| + 4 can be simplified based on different ranges of x: - For x < 1, the equation simplifies to -3x + 6. - For 1 ≤ x < -2, the equation simplifies to -3. - For -2 ≤ x < 3, the equation simplifies to 2x + 8. - For x ≥ 3, the equation simplifies to 3x + 2.