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How do you solve #|x - 10| = 3#?

Answer 1

See a solution process below:

The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

Solution 1:

#x - 10 = -3#

#x - 10 + color(red)(10) = -3 + color(red)(10)#

#x - 0 = 7#

#x = 7#

Solution 2:

#x - 10 = 3#

#x - 10 + color(red)(10) = 3 + color(red)(10)#

#x - 0 = 13#

#x = 13#

The Solution Set Is: #x = {7, 13}#

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Answer 2

Julia Adams

To solve the equation (|x - 10| = 3), you have two cases:

When (x - 10) is positive or zero: (x - 10 = 3) (x = 3 + 10) (x = 13)
When (x - 10) is negative: (-(x - 10) = 3) (-x + 10 = 3) (-x = 3 - 10) (-x = -7) (x = -7) (Divide both sides by -1)

So the solutions are (x = 13) and (x = -7).

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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.