-(-2 + 1)

-(-1)

1.

This gave us the same answer as the absolute value expression. Why? Because thats what the absolute value symbols mean. When the value is negative (less then 0) the sign is reversed to make if positve.

Thus if (x < 0) |x| = -x

]]>Lets see, if x < 1 then the expression |x -1| will be - (x-1). If x > 4, then |8 - x| will be -(8 - 2x). Fortunatly, x can never be both less then 1 and greater then 4 so its either one or the other. Not both. Of course, if x is neither less then 1, nor greater then 4, then both the abolute value symbols can be eliminated. So lets check all three situations.

if x < 1

-(x - 1) - ( 8 - 2x) = 3 solved x = 10. 10 is not less then 1 so we discard this solution.

if (x > 4)

(x - 1) + (8 - 2x) = 3 solved x = 4. 4 is not less then 4 so we discard this solution.

if (1 <= x <=4)

(x - 1) - (8 - 2x) = 3. solved x = 4. 4 is greater then 1 and less then 4 so this is an acceptable solution.

So if my thinking is correct, x = 4 should be the solution.

]]>| X - 1 | - | 8 - 2x | = 3

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