Question

|x|+|4-x|+|x-5|=12 ​

Answer 1

Уравнение:

Ответ:

x=-1 x=7

Answer 2

To solve the equation |x| + |4-x| + |x-5| = 12, we need to consider different cases based on the possible values of x. The absolute value function produces different results depending on whether the argument is positive, negative, or zero. Let's break down the equation by considering different intervals for x:

1. When x ≥ 5: In this case, all three absolute values are equal to their arguments since x is greater than or equal to 5. So we have: x + (4 - x) + (x - 5) = 12 Solving for x: x + 4 - x + x - 5 = 12 0 = 13 (This is not possible.)

2. When 4 ≤ x < 5: In this case, the absolute value of (x - 5) is equal to (5 - x), and the other absolute values are equal to their arguments: x + (4 - x) + (5 - x) = 12 Solving for x: x + 4 - x + 5 - x = 12 9 - x = 12 -x = 3 x = -3 (But this value does not satisfy the original interval.)

3. When 0 ≤ x < 4: In this case, all three absolute values are equal to their arguments: x + (4 - x) + (x - 5) = 12 Solving for x: x + 4 - x + x - 5 = 12 -1 = 12 (This is not possible.)

4. When x < 0: In this case, the absolute value of x is equal to -x, and the other absolute values are equal to their arguments: -x + (4 - x) + (x - 5) = 12 Solving for x: -x + 4 - x + x - 5 = 12 -x - 1 = 12 -x = 13 x = -13 (This value satisfies the original equation.)

Therefore, the solution to the equation |x| + |4-x| + |x-5| = 12 is x = -13.