Question

1;|х+1|+5=3 2;|х+5|-2=7

Answer 1

|x+1|+5=3
|x+1|=3-5
|x+1|=-2
xє пустое множество

|x+5|-2=7
|x+5|=9
—
|x+5=9
|x+5=-9
—
—
|x=4
|x=-14
—
xє{4;-14}

Answer 2

Ответ: 1) |х+1|=-2 нет решения.

2) |х+5|=9 или х1=4, х2=-9-5=-14

.

Пошаговое объяснение:

Answer 3

Let's solve the equations step by step:

1. |x + 1| + 5 = 3

To eliminate the absolute value, we'll consider two cases:

Case 1: x + 1 is positive or zero (x + 1 ≥ 0) In this case, the equation becomes: x + 1 + 5 = 3 x + 6 = 3 x = 3 - 6 x = -3

Case 2: x + 1 is negative (x + 1 < 0) In this case, the equation becomes: -(x + 1) + 5 = 3 (we negate the absolute value by adding a negative sign) -x - 1 + 5 = 3 -x + 4 = 3 -x = 3 - 4 -x = -1 Multiplying both sides by -1 (to solve for x): x = 1

Therefore, the solutions to the first equation are x = -3 and x = 1.

2. |x + 5| - 2 = 7

Again, we'll consider two cases:

Case 1: x + 5 is positive or zero (x + 5 ≥ 0) In this case, the equation becomes: x + 5 - 2 = 7 x + 3 = 7 x = 7 - 3 x = 4

Case 2: x + 5 is negative (x + 5 < 0) In this case, the equation becomes: -(x + 5) - 2 = 7 -x - 5 - 2 = 7 -x - 7 = 7 -x = 7 + 7 -x = 14 Multiplying both sides by -1 (to solve for x): x = -14

Therefore, the solutions to the second equation are x = 4 and x = -14.

In summary: For the first equation, the solutions are x = -3 and x = 1. For the second equation, the solutions are x = 4 and x = -14.