Question

1)|x| = 32)|x -3| = 23)|x - 4| = 0

Answer 1

1) |х| = 3
x = 3 или х = -3
2) |х - 3| = 2
х - 3 = 2 или х - 3 = -2
Тогда:
х = 5 или х = 1
3) |х - 4| = 0
х - 4 = 0
х = 4

Answer 2

Let's solve each of the equations one by one:

1. |x| = 3

The absolute value of a number is always positive or zero, so we have two cases to consider:

Case 1: x is positive or zero. If x is greater than or equal to 0, then |x| = x. So the equation becomes x = 3. The solution in this case is x = 3.

Case 2: x is negative. If x is less than 0, then |x| = -x. So the equation becomes -x = 3. To isolate x, we multiply both sides by -1, which changes the sign: x = -3. The solution in this case is x = -3.

Therefore, the solutions to the equation |x| = 3 are x = 3 and x = -3.

2. |x - 3| = 2

Again, we have two cases to consider:

Case 1: x - 3 is positive or zero. If x - 3 is greater than or equal to 0, then |x - 3| = x - 3. So the equation becomes x - 3 = 2. Solving for x, we add 3 to both sides: x = 5. The solution in this case is x = 5.

Case 2: x - 3 is negative. If x - 3 is less than 0, then |x - 3| = -(x - 3). So the equation becomes -(x - 3) = 2. Expanding the negative sign, we get -x + 3 = 2. To isolate x, we subtract 3 from both sides: -x = -1. Multiplying both sides by -1 to change the sign, we get x = 1. The solution in this case is x = 1.

Therefore, the solutions to the equation |x - 3| = 2 are x = 5 and x = 1.

3. |x - 4| = 0

The absolute value of any number is 0 only when the number itself is 0. Therefore, we have:

x - 4 = 0 Solving for x, we add 4 to both sides: x = 4.

The solution to the equation |x - 4| = 0 is x = 4.