Question 68285This question is from textbook
: Solve the equation |X + 11| = |2X + 5|
Here is what I have tried so far but it is not matching to any answer I have.
x + 11 = - 2x + 5 and -x +11 = 2x + 5
with this my answer are x=-2 and x=-6 but they are not correct
This question is from textbook
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Solve the equation |X + 11| = |2X + 5|
Since absolute value has different meaning, depending on whether
the inner expression is positive or negative, you have to start
by finding the zero values of the inner expressions.
If x+11=0 then x=-11
If 2x+5=0 then x=-5/2
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Mark these two values on a number line thus creating three intervals.
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Now check for solutions in each of the intervals (-inf,-11),(-11,-5/2),
and (-5/2,inf).
If x=-100 your equation becomes -(x+11) = -(22x-5); 21x=16; x = 16/21
If x=-8 your equation becomes x+11=-(2x+5); 3x=-16; x=-16/3
If x=100 your equation becomes x+11=2x+5 which gives x=16/21
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Conclusion: x=16/21 or x=-16/3
Cheers,
Stan H.
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