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How do you solve #|3x - 5|+ 4= 1#?

Answer 1

No solutions.

#|3x - 5| + 4 = 1#

First, we need to make the value in the absolute value by itself. So subtract #4# from both sides of the equation: #|3x - 5| = -3#

Now, we set the value inside the absolute value equal to the other side, and the opposite of the other side.

So we do: #3x - 5 = -3# AND #3x - 5 = 3#

#3x = 2# #quadquadquadquadquadquad# AND #quadquadquadquad3x = 8#

#x = 2/3# #quadquadquadquadquadquad# AND #quadquadquadquadquadx = 8/3#

#x = 2/3,# #8/3#

However, we need to check our solutions and see if they really work by plugging them in to the original equation: #|3x-5| + 4= 1#

#|3x - 5| = -3#

Instead of plugging in the solutions, we can actually see that an absolute value CANNOT equal to a negative number, so the answer is actually no solution.

Hope this helps!

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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.