Question

5) |x+3|+4=9 6) |y-2|+8=5 | | это модуль

Answer 1

Ответ:

5)x=2

  x= -8

6)Утверждение ложно, функция модуля всегда положительна.

Пошаговое объяснение:

5) |x-3|+4=9

|x+3|=5

x+3=5

x+3= -5

x=2

x= -8

6) |y-2|+8=5

|y-2|= -3

Утверждение ложно, функция модуля всегда положительна.

Answer 2

Yes, | | denotes the absolute value or modulus in mathematics. The absolute value of a number is its distance from zero on the number line, always resulting in a non-negative value.

Let's solve the given equations:

5. |x + 3| + 4 = 9

To solve for x, first, we need to isolate the absolute value term. Subtract 4 from both sides:

|x + 3| = 9 - 4

|x + 3| = 5

Now, we have two cases to consider:

Case 1: x + 3 is positive: If x + 3 is positive, then |x + 3| is equal to x + 3. So we can write the equation as:

x + 3 = 5

Now, solve for x:

x = 5 - 3

x = 2

Case 2: x + 3 is negative: If x + 3 is negative, then |x + 3| is equal to -(x + 3). So we can write the equation as:

-(x + 3) = 5

Now, solve for x:

x + 3 = -5

x = -5 - 3

x = -8

Thus, the solutions for the equation are x = 2 and x = -8.

6. |y - 2| + 8 = 5

To solve for y, first, we need to isolate the absolute value term. Subtract 8 from both sides:

|y - 2| = 5 - 8

|y - 2| = -3

Since the absolute value can never be negative, there are no solutions for this equation.

In conclusion: 5) The solutions for the equation |x + 3| + 4 = 9 are x = 2 and x = -8.

6. There are no solutions for the equation |y - 2| + 8 = 5.