Question

Number of sol. Of equation x-/4-x/-
2x=4 is

Answer 1

Answer:

You have |x−|4−x||−2x=4

Rewrite it as   |x−|4−x||=4+2x.

Since the absolute values is not negative it implies that  4+2x≥0, i.e.  x≥−2.

So we have either:

x≥−2.

x−|4−x|=−4−2x.

or

x≥−2.

x−|4−x|=4+2x

Now repeat the above trick:

|4−x|=3x+4(1)

or

|4−x|=−4−x(2)

For (1) we have   x≥−43.  

Recall that x≥−2, so    x≥−43  is OK.

For (2) holds for all −4−x≥0, i.e. x≤−4  Recall, that x≥−2. Hence  it has no solutions.

Now (1)  is equivalent to  4−x=±(3x+4), i.e. 4−x+3x+4=0, or  4−x−3x−4=0.  Thus x=−4 or x=0.  Only x=0 satisfies the inequality x≥−2.

Thus  the answer is  x=0.

Step-by-step explanation:

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