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How do you solve #abs(x+3)=abs(6x+9)#?

Answer 1

Isaiah Anthony

#-6/5#and #-12/7#

Or the expressions inside the brachets are equal, or they are symmetric:

#|x+3|=|6x+9|#

1) #x+3=6x+9#

#-5x=6#

#x=-6/5

2) #x+3=-(6x+9)#

#x+3=-6x-9)#

#7x=-12#

#x=-12/7#

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Answer 2

Nathan Axel

To solve the equation (|x + 3| = |6x + 9|), you'll need to consider both the positive and negative cases for the absolute values.

Positive Case: (x + 3 = 6x + 9) Solve for (x): (5x = -6) (x = -\frac{6}{5})

Negative Case: (x + 3 = -(6x + 9)) Solve for (x): (x + 3 = -6x - 9) (7x = -12) (x = -\frac{12}{7})

So, the solutions to the equation are (x = -\frac{6}{5}) and (x = -\frac{12}{7}).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.