Question

Solve:

Answer 1

1)

2 - 4| x + 2 |  ≥  - 6

- 4| x + 2 |  ≥  - 6 - 2

- 4| x + 2 |  ≥  - 8

- 4| x + 2 |  ≥  - 8

Multiply total inequality with "-1" and flip the symbol

4| x + 2 |  <=   8

| x + 2 |  <=   8/4

| x + 2 |  <=   2

-2  <=  x + 2  <=  2

-2 - 2  <=  x  <=  2 - 2

-4  <=  x  <=  0

2)

-3 - |5 - 2x|  <  - 11

- |5 - 2x|  <  - 11 + 3

- |5 - 2x|  <  - 8

Multiply total inequality with "-1" and flip the symbol

|5 - 2x|  >   8

5 - 2x >   8     or     5 - 2x  <  - 8

- 2x >   8 - 5    or   - 2x  <  - 8 - 5

- 2x >   3    or   - 2x  <  - 13

Multiply total inequality with "-1" and flip the symbol

2x <  - 3    or    2x  >   13

x <  - 3/2    or    x  >   13/2

Answer :

1) The Solution is -4  <=  x  <=  0

2)  The Solution is x <  - 3/2    or    x  >   13/2.