Asked by Ivan
Solve the equation: |6x - 2| = |3x + 1|
Answers
Answered by
Reiny
6x-2 = 3x+1 OR 6x-2 = -3x - 1
3x= 3 OR 9x = 1
x = 1 OR x = 1/9
3x= 3 OR 9x = 1
x = 1 OR x = 1/9
Answered by
Ivan
Thanks Reiny
Answered by
Steve
Recall that
|n| = n if n >= 0
|n| = -n if n < 0
So, you have four cases to consider:
(6x-2) >= 0
(6x-2) < 0
(3x+1) >= 0
(3x+1) < 0
In pairing up the conditions, some may be incompatible.
On the other hand, while the expressions may be positive or negative, their square will always be positive. So, we can just as easily say
(6x-2)^2 = (3x+1)^2
9x^2 - 10x + 1 = 0
(x-1)(9x-1) = 0
x = 1/9 or 1
This makes sense, since you rec all the graphs are v-shapes sitting side by side. Since one is steeper than the other, they may well cross in two places.
See that graphs at
http://www.wolframalpha.com/input/?i=solve+|6x+-+2|+%3D+|3x+%2B+1|
|n| = n if n >= 0
|n| = -n if n < 0
So, you have four cases to consider:
(6x-2) >= 0
(6x-2) < 0
(3x+1) >= 0
(3x+1) < 0
In pairing up the conditions, some may be incompatible.
On the other hand, while the expressions may be positive or negative, their square will always be positive. So, we can just as easily say
(6x-2)^2 = (3x+1)^2
9x^2 - 10x + 1 = 0
(x-1)(9x-1) = 0
x = 1/9 or 1
This makes sense, since you rec all the graphs are v-shapes sitting side by side. Since one is steeper than the other, they may well cross in two places.
See that graphs at
http://www.wolframalpha.com/input/?i=solve+|6x+-+2|+%3D+|3x+%2B+1|
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