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Đáp án:

`a) \sqrt{0,81} . (|x + 1| + \sqrt{16/144}) = 9/10`

    `0,9 . (|x + 1| + 1/3) = 9/10`

    `|x + 1| + 1/3 = 1`

    `|x + 1| = 2/3`

`Th1:`

`x + 1 = 2/3`

`x = -1/3`

`Th2:`

`x + 1 = -2/3`

`x = -5/3`

Vậy `x \in {-1/3 ; -5/3}`

`b) |1/3 . \sqrt{x + 1} - 2/9| - 1/6 = 1/9`

    `|1/3 . \sqrt{x + 1} - 2/9| = 5/18`

`Th1:`

`1/3 . \sqrt{x + 1} - 2/9 = 5/18`

`1/3 . \sqrt{x + 1} = 1/2`

`\sqrt{x + 1} = 3/2`

`x + 1 = 9/4`

`x = 5/4`

`Th2:`

`1/3 . \sqrt{x + 1} - 2/9 = -5/18`

`1/3 . \sqrt{x + 1} = -1/18`

`\sqrt{x + 1} = -1/6 (`vô lý`)`

Vậy `x = 5/4`

`c) |2x - 1| = 3`

`Th1:`

`2x - 1 = 3`

`2x = 4`

`x = 2`

`Th2:`

`2x - 1 = -3`

`2x = -2`

`x = -1`

Vậy `x \in {2 ; -1}`

`d) |3x - 2| = |x|`

    `3x - 2 = x`

`Th1:`

`3x - 2 = x`

`3x - 2 - x = 0`

`2x - 2 = 0`

`2x = 2`

`x = 1`

`Th2:`

`3x - 2 = -x`

`3x - 2 + x = 0`

`4x - 2 = 0`

`4x = 2`

`x = 1/2`

Vậy `x \in {1 ; 1/2}`