Question

1) |x|-4=-8 2) |x-5|=5 3) |x-5|=4 4) ||x+5|-2|=0

Answer 1

Ответ:

1)х1=-4

х2=4

2)х1=10

х2=0

3)х1=9

х2=1

4)х=-3

Answer 2

Ответ:

Пошаговое объяснение:
1)
|х| - 4 = -8
|х| = -8 + 4
|х | = -4
Нет корней так как модуль числа всегда положительный или равен нулю
х € 0

2)
|х - 5| = 5
1)
х - 5 = 5
х = 5 + 5
х 1 = 10

2)
х - 5 = -5
х = -5 + 5
х2 = 0


3)
|х - 5| = 4
1)
х - 5 = 4
х = 4 + 5
х1 = 9

2)
х - 5 = -4
х = -4 + 5
х2 = 1


4)
||х + 5| - 2| = 0
|х + 5| - 2 = 0
|х + 5| = 2
1)
х + 5 = 2
х = 2 - 5
х1 = -3

2)
х + 5 = -2
х = -2 - 5
х2 = -7

Answer 3

Let's solve each of these absolute value equations step by step:

1. |x| - 4 = -8:

Add 4 to both sides of the equation: |x| = -8 + 4 |x| = -4

Absolute values are always non-negative, so there are no solutions to this equation.

2. |x - 5| = 5:

This equation has two cases, one for when x - 5 is positive and one for when x - 5 is negative.

Case 1: x - 5 is positive: x - 5 = 5

Add 5 to both sides: x = 5 + 5 x = 10

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

Multiply both sides by -1 to get rid of the negative sign: x - 5 = -5

Add 5 to both sides: x = -5 + 5 x = 0

So, there are two solutions: x = 10 and x = 0.

3. |x - 5| = 4:

Again, we have 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: x - 5 = -4

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

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

4. ||x + 5| - 2| = 0:

Let's break it down into two cases.

Case 1: |x + 5| - 2 is positive: |x + 5| - 2 = 0

Add 2 to both sides: |x + 5| = 2

Now, we have two sub-cases.

Sub-case 1.1: x + 5 is positive: x + 5 = 2

Subtract 5 from both sides: x = 2 - 5 x = -3

Sub-case 1.2: x + 5 is negative: -(x + 5) = 2

Multiply both sides by -1: x + 5 = -2

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

So, there are two solutions for this case: x = -3 and x = -7.

Case 2: |x + 5| - 2 is negative: |x + 5| - 2 = 0 is not possible since absolute values are always non-negative. So, there are no solutions in this case.

Overall, the solutions are x = 10, x = 0, x = 9, x = 1, x = -3, and x = -7.