Question

1)|х|=7. 2)|х+2|=3. 3)|х-3|=0 4)|х+4|=-3. 5)|х|+3=9​

Answer 1

Пошаговое объяснение:

1)|x|=7

x=-7;7

2)|x+2|=3

x+2=3

x=1

x+2=-3

x=-5

3)|x-3|=0

x=3

4)|x+4|=-3

корней нет,потому-что модуль не может быть отрицательный

5)|x|+3=9

|x|=6

x=-6,6

Answer 2

To solve these absolute value equations, you'll need to consider both the positive and negative cases for the absolute value expression. Here are the solutions for each of the equations:

1. |x| = 7

Positive case: x = 7

Negative case: x = -7

So, the solutions are x = 7 and x = -7.

2. |x + 2| = 3

Positive case: x + 2 = 3 x = 3 - 2 x = 1

Negative case: -(x + 2) = 3 x + 2 = -3 x = -3 - 2 x = -5

So, the solutions are x = 1 and x = -5.

3. |x - 3| = 0

In this case, the absolute value of any number is always non-negative, so it can never be equal to 0. Therefore, there are no solutions to this equation.

4. |x + 4| = -3

Again, the absolute value of any number is always non-negative, so it can never be equal to -3. Therefore, there are no solutions to this equation.

5. |x| + 3 = 9

Subtract 3 from both sides:

|x| = 9 - 3 |x| = 6

Positive case: x = 6

Negative case: x = -6

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