Question

1) |x + 3| = -42) |x| + 1 = 73)|x| - 2 = -3

Answer 1

1) |х+3|=-4(это ложное утверждение)
2) |х|+1=7
|х|=7-1
|х|=6
Окончательный ответ:х1=-6;х2=6
3) |х|-2=-3
|х|=-3+2
|х|=-1(это ложное утверждение)

Answer 2

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

1. |x + 3| = -4

Since the absolute value of any real number is always non-negative, it can never be negative, there is no solution for this equation. The absolute value of any expression is always greater than or equal to zero.

2. |x| + 1 = 7

Subtract 1 from both sides:

|x| = 7 - 1 |x| = 6

Now, we have two cases for the absolute value:

Case 1: x is positive or zero: If x is positive or zero, then |x| = x, so we can write: x = 6

Case 2: x is negative: If x is negative, then |x| = -x, so we can write: -x = 6

Multiply both sides by -1 (to isolate x): x = -6

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

3. |x| - 2 = -3

Add 2 to both sides:

|x| = -3 + 2 |x| = -1

Again, the absolute value of any expression is always non-negative, so it can never be negative. Thus, there is no solution for this equation.

In summary:

1. No solution
2. x = 6 and x = -6
3. No solution