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How do you solve #abs(2x+13)=28#?

Answer 1

Hazel Anglin

The solution is #x = 7.5, -20.5#

Removing the absolute value function and solving these two equations provide the answer:

#2x + 13 = 28 => #2x + 13 - 13 = 28 - 13 => 2x = 15 => x = 7.5#

#2x + 13 = -28 => 2x + 13 - 13 = -28 - 13 => 2x = -41 => x = -20.5#

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Answer 2

Isaiah Anthony

To solve the equation (|2x + 13| = 28), you split it into two cases:

Case 1: (2x + 13 = 28) Solve for (x): (2x = 28 - 13) (2x = 15) (x = \frac{15}{2})

Case 2: (2x + 13 = -28) Solve for (x): (2x = -28 - 13) (2x = -41) (x = \frac{-41}{2})

Therefore, the solutions are (x = \frac{15}{2}) and (x = \frac{-41}{2}).

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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.