Question

3.Розв’яжи рівняння: 1) |x|+ 4 = –5; 2) 5 – |x|= –2; 3) |x – 5| = 4.

Answer 1

Ответ:

Пошаговое объяснение:

1) |x|+ 4 = –5

|x|=-5-4=-9

Уравнение не имеет решений, так как модуль не может быть отрицательным.

2) 5-|x|=-2

|x|=5+2

x=±7

Ответ: -7; 7.

3) |x-5|=4

При x-5≥0:

x-5=4

x₁=4+5=9

При x-5<0:

5-x=4

x₂=5-4=1

Ответ: 1; 9.

Answer 2

1. |x| + 4 = -5:

Subtract 4 from both sides: |x| = -5 - 4 |x| = -9

The absolute value of any real number is always non-negative, so there are no solutions to this equation.

2. 5 - |x| = -2:

Subtract 5 from both sides: -|x| = -2 - 5 -|x| = -7

Multiply both sides by -1 to isolate |x|: |x| = 7

Now, there are two possible solutions: x = 7 and x = -7.

3. |x - 5| = 4:

To solve this equation, we can split it into two cases:

Case 1: (x - 5) is positive: x - 5 = 4

Add 5 to both sides: x = 4 + 5 x = 9

Case 2: (x - 5) is negative: -(x - 5) = 4

Multiply both sides by -1 to isolate (x - 5): x - 5 = -4

Add 5 to both sides: x = -4 + 5 x = 1

So, there are two solutions: x = 9 and x = 1.