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

Answer 1

Eva Adamson

#x = 4/3 or x = -4#

So the absolute value is either #3x+4# or #-(3x+4)#.

So:

#3x+4-5 = 3" " or " "-3x-4-5 =3#

# 3x -1 = 3 " " or" " -3x -9 =3#

# 3x = 4" " or" " -3x = 12#

#x= 4/3 " "or " "x = -4#

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Answer 2

Nathan Axel

To solve the equation (|3x + 4| - 5 = 3), follow these steps:

Add 5 to both sides of the equation to isolate the absolute value term: (|3x + 4| = 8).
Now, there are two cases to consider: a) (3x + 4 = 8), and b) (3x + 4 = -8).
Solve each case separately: a) For (3x + 4 = 8), subtract 4 from both sides and solve for x. b) For (3x + 4 = -8), subtract 4 from both sides and solve for x.
After finding the solutions for each case, verify them by substituting back into the original equation to ensure they satisfy the equation.

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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.