Multiple choice

Solve the equation $ \left| x-\left| 4-x \right| \right| -2x=4$

  1. $x=0$
  2. $x=1$
  3. $x=2$
  4. $x=3$
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A Correct answer
Explanation

Test x=0: |0 - |4-0|| - 2(0) = |-4| - 0 = 4. This matches the equation. Other options like x=1 result in |1 - 3| - 2 = 2 - 2 = 0, not 4.

AI explanation

The absolute value equation is solved by testing intervals based on the critical value x equals 4. Testing the condition where x is less than 4, the inner absolute value expression (4 minus x) remains positive, making the equation the absolute value of (x minus (4 minus x)) minus 2x equals 4. When x is between 0 and 4, x minus (4 minus x) is positive, so removing the absolute value gives (2x minus 4) minus 2x equals 4, which simplifies to negative 4 equals 4, an invalid statement. When x is less than 0, x minus (4 minus x) is negative, so removing the absolute value gives negative (2x minus 4) minus 2x equals 4, which simplifies to negative 4x equals 0, yielding x equals 0.

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