Question

Розв'яжіть рівняння1. |х|=62. 4-2|х|=0,23. ||х|+4|=7​

Answer 1

Ответ:

|×|=6

х=6

х=-6

-2|×|=0,2-4

-2|×|=-3,8

|×|=1,9

х=1,9

х=-1,9

||×|+4|=7

|×|=7-4

|×|=3

х=3

х=-3

Answer 2

1. |x| = 62: To solve this equation, we consider two cases: when x is positive and when x is negative.

   Case 1: x is positive If x is positive, then |x| = x, so the equation becomes x = 62. Solving for x, we have x = 62.

   Case 2: x is negative If x is negative, then |x| = -x, so the equation becomes -x = 62. Solving for x, we have x = -62.

   Therefore, the solution to the equation |x| = 62 is x = 62 or x = -62.

2. 4 - 2|x| = 0.23: We again consider two cases: when x is positive and when x is negative.

   Case 1: x is positive If x is positive, then |x| = x, so the equation becomes 4 - 2x = 0.23. Solving for x, we have x = (4 - 0.23) / 2 = 1.885.

   Case 2: x is negative If x is negative, then |x| = -x, so the equation becomes 4 + 2x = 0.23. Solving for x, we have x = (0.23 - 4) / 2 = -1.885.

   Therefore, the solution to the equation 4 - 2|x| = 0.23 is x = 1.885 or x = -1.885.

3. ||x| + 4| = 7: Let's consider two cases: when x + 4 is positive and when x + 4 is negative.

   Case 1: x + 4 is positive If x + 4 is positive, then |x + 4| = x + 4, so the equation becomes x + 4 = 7. Solving for x, we have x = 7 - 4 = 3.

   Case 2: x + 4 is negative If x + 4 is negative, then |x + 4| = -(x + 4), so the equation becomes -(x + 4) = 7. Solving for x, we have x = -7 - 4 = -11.

   Therefore, the solution to the equation ||x| + 4| = 7 is x = 3 or x = -11.