How do you solve abs(2x - 6) = abs(x +7) - 3 ?

1 Answer
Narad T.
Jun 30, 2018

The solutions are S={2/3,10}

Explanation:

The equation is

|2x-6|=|x+7|-3

=>, |2x-6|-|x+7|+3=0

The points to be considered are when

{(2x-6=0),(x+7=0):}

=>, {(x=3),(x=-7):}

There are 3 cases to consider

In the interval (-oo, -7)

2x-6-(-x-7)+3=0

=>, 2x-6+x+7+3=0

=>, 3x+4=0

=>, x=-4/3

This solution is not possible since x=-4/3 !in to (-oo,-7)

In the interval (-oo, -7)

-2x+6-(x+7)+3=0

=>, -2x+6-x-7+3=0

=>, -3x+2=0

=>, x=2/3

This solution is possible since x=2/3 in to (-7,3)

In the interval (3,+oo)

2x-6-(x+7)+3=0

=>, 2x-6-x-7+3=0

=>, x-10=0

=>, x=10

This solution is possible since x=10 in to (3,+oo)

The solutions are S={2/3,10}

graph{|2x-6|-|x+7|+3 [-18.02, 18.03, -9.01, 9.01]}

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