Question

|2х+14|=6|9х-18|=27|8х+12|=20|15х-10|=5|9х+15|=6|8х-6|=14​

Answer 1

Ответ:

|2х+18|=6 |9х-18|=27

2х=14-6 9х=18+27

2х=8 9х=45

х=8:2 х=45:9

х=-4 х=5

Answer 2

To solve the given system of equations, let's solve each equation separately:

1. |2x + 14| = 6:

   For 2x + 14 > 0: 2x + 14 = 6 2x = 6 - 14 2x = -8 x = -4

   For 2x + 14 < 0: -(2x + 14) = 6 -2x - 14 = 6 -2x = 6 + 14 -2x = 20 x = -10

   So the possible values of x for this equation are -4 and -10.

2. |9x - 18| = 27:

   For 9x - 18 > 0: 9x - 18 = 27 9x = 27 + 18 9x = 45 x = 5

   For 9x - 18 < 0: -(9x - 18) = 27 -9x + 18 = 27 -9x = 27 - 18 -9x = 9 x = -1

   So the possible values of x for this equation are 5 and -1.

3. |8x + 12| = 20:

   For 8x + 12 > 0: 8x + 12 = 20 8x = 20 - 12 8x = 8 x = 1

   For 8x + 12 < 0: -(8x + 12) = 20 -8x - 12 = 20 -8x = 20 + 12 -8x = 32 x = -4

   So the possible values of x for this equation are 1 and -4.

4. |15x - 10| = 5:

   For 15x - 10 > 0: 15x - 10 = 5 15x = 5 + 10 15x = 15 x = 1

   For 15x - 10 < 0: -(15x - 10) = 5 -15x + 10 = 5 -15x = 5 - 10 -15x = -5 x = 1/3

   So the possible values of x for this equation are 1 and 1/3.

5. |9x + 15| = 6:

   For 9x + 15 > 0: 9x + 15 = 6 9x = 6 - 15 9x = -9 x = -1

   For 9x + 15 < 0: -(9x + 15) = 6 -9x - 15 = 6 -9x = 6 + 15 -9x = 21 x = -7/3

   So the possible values of x for this equation are -1 and -7/3.

6. |8x - 6| = 14:

   For 8x - 6 > 0: 8x - 6 = 14 8x = 14 + 6 8x = 20 x = 5/2

   For 8x - 6 < 0: -(8x - 6) = 14 -8x + 6 = 14 -8x = 14 - 6 -8x = 8 x = -1

   So the possible values of x for this equation are 5/2 and -1.

Therefore, the solutions to the system of equations are: x = -10, -4, -1, 1/3, 1, 5/2.