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

1 Answer
smendyka
Mar 13, 2018

See a solution process below:

Explanation:

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 + 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

Solution 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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