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

Answer 1

See the entire solution process below:

We must solve the term within the absolute value function for both its negative and positive equivalent because the absolute value function takes any term, whether positive or negative, and converts it to its positive form.

First Solution

#x + 3 = -5#

#x + 3 - color(red)(3) = -5 - color(red)(3)#

#x + 0 = -8#

#x = -8#

Option 2)

#x + 3 = 5#

#x + 3 - color(red)(3) = 5 - color(red)(3)#

#x + 0 = 2#

#x = 2#

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Answer 2

Ethan Adkins

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

Recognize that the absolute value of (x + 3) could equal 5 or -5.
Set up two equations based on these possibilities:

a) (x + 3 = 5)

b) (x + 3 = -5)

Solve each equation separately:

a) For (x + 3 = 5):

Subtract 3 from both sides:

\(x = 5 - 3\)

\(x = 2\)

b) For (x + 3 = -5):

Subtract 3 from both sides:

\(x = -5 - 3\)

\(x = -8\)

So, the solutions to the equation are (x = 2) and (x = -8).

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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.