Question

1)|x-4|=2 2)|y+5|=33)|3+x|=1,54)|7-y|=-25)|x+3|+4=96)|y-2|+8=5​

Answer 1

1) |x-4|=2
x-4=2
x-4=-2
x=6
x=2
Ответ:х1=2,х2=6
2)|у+5|=3
у+5=3
у+5=-3
у=-2
у=-8
Ответ: у1=-2, у2=-8
3)|3+х|=1,5
3+х=1,5
3+х=-1,5
3+х=-1,5
3+х=-4,5
Ответ:х1=-1,5;Х2=-4,5
4)|7-у|=-2
Утверждение ложно, так как функция модуля должна быть всегда положительна, либо 0

5)|х+3|+4=9
|х+3|=9-4
|х+3|=5
х+3=5
х+3=-5
х=2
х=-8
Ответ:х1=2,х2=-8
6)|у-2|+8=5
Утверждение также ложно

Answer 2

To solve each of these absolute value equations, you'll need to consider two cases for each equation: one where the expression inside the absolute value bars is positive, and one where it's negative. Here are the solutions for each of the equations:

1. |x - 4| = 2

Case 1: x - 4 = 2 x = 2 + 4 x = 6

Case 2: -(x - 4) = 2 -x + 4 = 2 -x = 2 - 4 -x = -2 x = 2

So, the solutions are x = 6 and x = 2.

2. |y + 5| = 3

Case 1: y + 5 = 3 y = 3 - 5 y = -2

Case 2: -(y + 5) = 3 -y - 5 = 3 -y = 3 + 5 -y = 8 y = -8

The solutions are y = -2 and y = -8.

3. |3 + x| = 1.54

Case 1: 3 + x = 1.54 x = 1.54 - 3 x = -1.46

Case 2: -(3 + x) = 1.54 -(3 + x) = 1.54 -3 - x = 1.54 -x = 1.54 + 3 -x = 4.54 x = -4.54

The solutions are x = -1.46 and x = -4.54.

4. |7 - y| = -25

Absolute values are never negative, so there are no real solutions for this equation.

5. |x + 3| + 4 = 9

First, subtract 4 from both sides:

|x + 3| = 5

Case 1: x + 3 = 5 x = 5 - 3 x = 2

Case 2: -(x + 3) = 5 -x - 3 = 5 -x = 5 + 3 -x = 8 x = -8

The solutions are x = 2 and x = -8.

6. |y - 2| + 8 = 5

First, subtract 8 from both sides:

|y - 2| = -3

Absolute values are never negative, so there are no real solutions for this equation.

So, for the given equations, there are solutions for equations 1, 2, 3, and 5, while equations 4 and 6 have no real solutions.