How do you solve #abs(-x+9)=4#?

Answer 1

See a solution process below:

Since the absolute value function takes any term and converts it to a non-negative form, we have to solve the term for both its positive and negative equivalent within the absolute value function.

First Solution:

#-x + 9 = -4#

#-x + color(red)(x) + 9 + color(red)(4) = -4 + color(red)(4) + color(red)(x)#

#0 + 13 = 0 + x#

#13 = x#

#x = 13#

Option 2:

#-x + 9 = 4#

#-x + color(red)(x) + 9 - color(red)(4) = 4 - color(red)(4) + color(red)(x)#

#0 + 5 = 0 + x#

#5 = x#

#x = 5#

The Solution Set Is: #x = {5, 13}#

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Answer 2

Eva Adamson

To solve the equation abs(-x+9)=4, you first isolate the absolute value expression. Then, you consider two cases: when the expression inside the absolute value is positive and when it is negative. Finally, you solve for x in each case.

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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.