The sum of five and some number #x# has an absolute value of 7. What are possible values of #x#?

1 Answer
Somebody N.
Sep 13, 2017

#x = 2# and #x = -12#

Explanation:

Because this is an absolute equation, we must solve for the expression in the absolute bars being both a positive value and a negative value. This is because the absolute value of a number is always positive. Consider the following.

#| 5 + x | = 7#

For positive value in bars we have:

#5 + x = 7 => x = 2#

For negative value in bars we have:

#| -( 5 + x ) | = 7#

Removing bars:

# -( 5 + x ) = 7#

# -5 - x = 7 => x = -12#

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