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

Answer 1

#x=-8" or "x=2#

#"the expression inside the absolute value can be positive"# #"or negative, hence there are 2 possible solutions"#
#x+3=color(red)(+-)5#
#x+3=5rArrx=5-3=2#
#x+3=-5rArrx=-5-3=-8#
#color(blue)"As a check"#

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

#x=2to|2+3|=|5|=5#
#x=-8to|-8+3|=|-5|=5#
#x=-8" or "x=2" are the solutions"#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To solve the equation |x + 3| = 5, you need to consider two cases: when the expression inside the absolute value is positive and when it is negative.

Case 1: x + 3 is positive: x + 3 = 5 x = 5 - 3 x = 2

Case 2: x + 3 is negative: -(x + 3) = 5 -x - 3 = 5 -x = 5 + 3 -x = 8 x = -8

So, the solutions to the equation |x + 3| = 5 are x = 2 and x = -8.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
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.

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.

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.

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.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7