To solve this equation, we first need to consider the absolute value expressions separately.
For |x-10|, we need to look at two cases: 1) When x-10 is positive: x-10 ≥ 0 → x ≥ 10 2) When x-10 is negative: x-10 < 0 → x < 10
Similarly, for |2-x|, we also need to consider two cases: 1) When 2-x is positive: 2-x ≥ 0 → x ≤ 2 2) When 2-x is negative: 2-x < 0 → x > 2
Now, we can substitute these cases back into the original equation:
For x ≥ 10 and x ≤ 2: 3x - (x-10) - (2-x) = -6 3x - x + 10 - 2 + x = -6 3x - x + x + 10 - 2 = -6 3x = -14 x = -14/3 (Not possible because x cannot be less than 2)
For x < 10 and x > 2: 3x - (x-10) - (2-x) = -6 3x - x + 10 - 2 + x = -6 3x - x + x + 10 - 2 = -6 3x = -14 x = -14/3 (Not possible because x cannot be less than 2)
Therefore, there are no solutions to the given equation.
To solve this equation, we first need to consider the absolute value expressions separately.
For |x-10|, we need to look at two cases:
1) When x-10 is positive: x-10 ≥ 0 → x ≥ 10
2) When x-10 is negative: x-10 < 0 → x < 10
Similarly, for |2-x|, we also need to consider two cases:
1) When 2-x is positive: 2-x ≥ 0 → x ≤ 2
2) When 2-x is negative: 2-x < 0 → x > 2
Now, we can substitute these cases back into the original equation:
For x ≥ 10 and x ≤ 2:
3x - (x-10) - (2-x) = -6
3x - x + 10 - 2 + x = -6
3x - x + x + 10 - 2 = -6
3x = -14
x = -14/3 (Not possible because x cannot be less than 2)
For x < 10 and x > 2:
3x - (x-10) - (2-x) = -6
3x - x + 10 - 2 + x = -6
3x - x + x + 10 - 2 = -6
3x = -14
x = -14/3 (Not possible because x cannot be less than 2)
Therefore, there are no solutions to the given equation.