Question

7. 1) |2x – 4) = 2; 2) \y + 5| = 3;3) |3+ x| = 1,5;4) |7 – y = -2;5) (x +3+ 4 = 9;6) \y – 21+ 8 = 5.​

Answer 1

Ответ:

Пример:2x=2+4

2x=6

x=3

Answer 2

It looks like you've provided a list of equations involving absolute values. I'll help you solve each of them:

1. |2x - 4| = 2: To solve for x, you can consider two cases: Case 1: 2x - 4 = 2 2x = 2 + 4 2x = 6 x = 6 / 2 x = 3

   Case 2: 2x - 4 = -2 (Note: when the absolute value equals a negative number, there are no solutions) 2x = -2 + 4 2x = 2 x = 2 / 2 x = 1

   So, the solutions are x = 3 and x = 1.

2. |y + 5| = 3: Again, consider two cases: Case 1: y + 5 = 3 y = 3 - 5 y = -2

   Case 2: -(y + 5) = 3 -y - 5 = 3 -y = 3 + 5 -y = 8 y = -8

   The solutions are y = -2 and y = -8.

3. |3 + x| = 1.5: Two cases: Case 1: 3 + x = 1.5 x = 1.5 - 3 x = -1.5

   Case 2: -(3 + x) = 1.5 -3 - x = 1.5 -x = 1.5 + 3 -x = 4.5 x = -4.5

   The solutions are x = -1.5 and x = -4.5.

4. |7 - y| = -2: There are no solutions because the absolute value of any real number is always non-negative, so it can't be equal to a negative number.

5. (x + 3 + 4 = 9: The equation appears to have a typo. It should be written as: x + 3 + 4 = 9 x + 7 = 9

   Now, solve for x: x = 9 - 7 x = 2

   The solution is x = 2.

6. |y - 21 + 8| = 5: Two cases: Case 1: y - 21 + 8 = 5 y - 13 = 5 y = 5 + 13 y = 18

   Case 2: -(y - 21 + 8) = 5 -y + 21 - 8 = 5 -y + 13 = 5 -y = 5 - 13 -y = -8 y = 8

   The solutions are y = 18 and y = 8.