Question

|x-2|+|x+2|=5 |6x+2|=4-5x

Answer 1

Пошаговое объяснение номер 1

Answer 2

Let's solve the given equations step-by-step:

1. |x - 2| + |x + 2| = 5

To solve this equation, we'll consider the different cases when the absolute values change signs.

Case 1: x - 2 ≥ 0 and x + 2 ≥ 0 In this case, both expressions inside the absolute values are non-negative, so the absolute values can be removed:

x - 2 + x + 2 = 5 2x = 5 x = 5/2

Case 2: x - 2 ≥ 0 and x + 2 < 0 Here, we have to change the sign inside the second absolute value:

x - 2 - (x + 2) = 5 x - 2 - x - 2 = 5 -4 = 5 (No solution in this case)

Case 3: x - 2 < 0 and x + 2 ≥ 0 Again, we change the sign inside the first absolute value:

-(x - 2) + (x + 2) = 5 -x + 2 + x + 2 = 5 4 = 5 (No solution in this case)

Case 4: x - 2 < 0 and x + 2 < 0 In this case, both expressions inside the absolute values are negative, so we remove the absolute values and change the signs:

-(x - 2) - (x + 2) = 5 -x + 2 - x - 2 = 5 -2x = 5 x = -5/2

So, we have two solutions: x = 5/2 and x = -5/2.

2. |6x + 2| = 4 - 5x

To solve this equation, we'll consider the different cases when the absolute value changes signs.

Case 1: 6x + 2 ≥ 0 In this case, the absolute value can be removed:

6x + 2 = 4 - 5x 11x = 2 x = 2/11

Case 2: 6x + 2 < 0 Here, we have to change the sign inside the absolute value:

-(6x + 2) = 4 - 5x -6x - 2 = 4 - 5x -x = 6 x = -6

So, we have two solutions: x = 2/11 and x = -6.