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How do you solve #abs(5x+2)= 3#?

Answer 1

when #(5x+2)>0,#then#|5x+2|=3=>5x+2=3=>x=1/5# when #(5x+2)<0,#then#|5x+2|=3=>-(5x+2)=3=>-5x=5=>x=-1# #:. x=1/5 #and #x=-1#

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Answer 2

Julia Adams

To solve the equation (|5x + 2| = 3), follow these steps:

Split the equation into two cases:
- Case 1: (5x + 2 = 3)
- Case 2: (5x + 2 = -3)
Solve each case separately:
- For Case 1: (5x + 2 = 3)
  - Subtract 2 from both sides: (5x = 1)
  - Divide both sides by 5: (x = \frac{1}{5})
- For Case 2: (5x + 2 = -3)
  - Subtract 2 from both sides: (5x = -5)
  - Divide both sides by 5: (x = -1)
Check the solutions:
- Substitute (x = \frac{1}{5}) into the original equation: (|5(\frac{1}{5}) + 2| = 3)
  - (|1 + 2| = 3)
  - (|3| = 3), which is true.
- Substitute (x = -1) into the original equation: (|5(-1) + 2| = 3)
  - (|(-5) + 2| = 3)
  - (|-3| = 3), which is also true.

Therefore, the solutions to the equation (|5x + 2| = 3) are (x = \frac{1}{5}) and (x = -1).

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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.