Question

Розв’яжіть рівняння: 2) | x| = 125; 3) | x |= 7,8; 4) |x| = 6 7 .

Answer 1

Ответ:

1)x=-125

x=125

3)x=–7,8

x=7.8

4) x=-6

x=6

Answer 2

$2)|x| = 125\\x=125\\x=-125\\x_1=125\\x_2=-125\\3)|x|= 7,8\\x=7,8\\x=-7,8\\x_1=7,8\\x_2=7,8\\4)|x| = 6\\x=6\\x=-6\\x_1=6\\x_2=-6$

Answer 3

1. |x| = 125

To solve this equation, we can consider two cases:

Case 1: x is positive: If x is positive, then |x| is equal to x. So we have: x = 125

Case 2: x is negative: If x is negative, then |x| is equal to -x. So we have: -x = 125

To solve this equation, we multiply both sides by -1: x = -125

Therefore, the solutions to the equation |x| = 125 are x = 125 and x = -125.

2. |x| = 7.8

Similarly, we consider two cases:

Case 1: x is positive: If x is positive, then |x| is equal to x. So we have: x = 7.8

Case 2: x is negative: If x is negative, then |x| is equal to -x. So we have: -x = 7.8

Again, we multiply both sides by -1: x = -7.8

Therefore, the solutions to the equation |x| = 7.8 are x = 7.8 and x = -7.8.

3. |x| = 6.7

Following the same approach:

Case 1: x is positive: If x is positive, then |x| is equal to x. So we have: x = 6.7

Case 2: x is negative: If x is negative, then |x| is equal to -x. So we have: -x = 6.7

Multiplying both sides by -1: x = -6.7

The solutions to the equation |x| = 6.7 are x = 6.7 and x = -6.7.